Database of accelerated collatz operators and cycles The accelerated 3n+r operator is defined by applying: (3n + r) / 2 when n is odd and n / 2 when n is even. Similarly, the accelerated 5n+r operator is defined by applying (5n + r) / 2 when n is odd n / 2 when n is even These operators constitute a natural accelerated analogue of the classical Collatz map, and play a fundamental role in understanding the core dynamical mechanisms underlying generalized problems. Although the definition of these transformations is elementary, their orbit structure continues to exhibit highly nontrivial behavior. The detection and classification of cycles in the accelerated framework is intimately connected to several persistent open problems, growth regimes for divergent orbits, and rigidity phenomena in one-dimensional discrete flows. These questions remain notoriously challenging, and the computational exploration of a range initial values provides essential insight into their qualitative behavior. We offer here an open, organized database of detected cycles for the accelerated and maps over the first 100000 n values for each subproblem. Parity notation:I = odd | P = even 3n+r problem Below are the first values of r from 1 to 7 with their corresponding cycles (for 1≤n≤100 000). A larger collection of values of r can be found below. 3n+1 n = 1 Cycle: {1, 2} | Length: 2 | Parity: IP (The Collatz problem has been verified up to 10^21 by Barina)3n+5 n = 1 Cycle: {1, 4, 2} | Length: 3 | Parity: IPP n = 5 Cycle: {5, 10} | Length: 2 | Parity: IP n = 3 Cycle: {19, 31, 49, 76, 38} | Length: 5 | Parity: IIIPP n = 23 Cycle: {23, 37, 58, 29, 46} | Length: 5 | Parity: IIPIP n = 123 Cycle: {187, 283, 427, 643, 967, 1453, 2182, 1091, 1639, 2461, 3694, 1847, 2773, 4162, 2081, 3124, 1562, 781, 174, 587, 883, 1327, 1993, 2992, 1496, 748, 374} | Length: 27 | Parity: IIIIIIPIIIPIIPIPPIPIIIIPPPP n = 171 Cycle: {347, 523, 787, 1183, 1777, 2668, 1334, 667, 1003, 1507, 2263, 3397, 5098, 2549, 3826, 1913, 2872, 1436, 718, 359, 541, 814, 407, 613, 922, 461, 694} | Length: 27 | Parity: IIIIIPPIIIIIPIPIPPPIIPIIPIP 3n+7n = 1 Cycle: {5, 11, 20, 10} | Length: 4 | Parity: IIPPn = 7 Cycle: {7, 14} | Length: 2 | Parity: IP More detailed tables and additional values of r and n can be found in the extended dataset 3n+r. See also a mirror in Link GitHub. 5n+r problem The accelerated 5n+r map is more delicate. Numerical evidence suggests the existence of trajectories that may not converge, making the detection of cycles more subtle. Below we present the first cases for small values of r. 5n+3 (n = 1 to 100000) n = 1 Cycle: {1, 4, 2} | Length: 3 | Parity: IPPn = 3 Cycle: {3, 9, 24, 12, 6} | Length: 5 | Parity: IIPPPn = 5 First possibly non-convergent orbit .n = 39 Cycle: {39, 99, 249, 624, 312, 156, 78} | Length: 7 | Parity: IIIPPPPn = 43 Cycle: {43, 109, 274, 137, 344, 172, 86} | Length: 7 | Parity: IIPIPPPn = 51 Cycle: {51, 129, 324, 162, 81, 204, 102} | Length: 7 | Parity: IIPPIPPn = 53 Cycle: {53, 134, 67, 169, 424, 212, 106} | Length: 7 | Parity: IPIIPPPn = 61 Cycle: {61, 154, 77, 194, 97, 244, 122} | Length: 7 | Parity: IPIPIPP 5n+7 (n = 1 to 100000) n = 1 Cycle: {1, 6, 3, 11, 31, 81, 206, 103, 261, 656, 328, 164, 82, 41, 106, 53, 136, 68, 34, 17, 46, 23, 61, 156, 78, 39, 101, 256, 128, 64, 32, 16, 8, 4, 2} | Length: 35 | Paridad: IPIIIIPIIPPPPIPIPPPIPIIPPIIPPPPPPPPn = 7 Cycle: {7, 21, 56, 28, 14} | Length: 5 | Paridad: IIPPPn = 9 Cycle: {9, 26, 13, 36, 18} | Length: 5 | Paridad: IPIPPn = 27 Cycle: {57, 146, 73, 186, 93, 236, 118, 59, 151, 381, 956, 478, 239, 601, 1506, 753, 1886, 943, 2361, 5906, 2953, 7386, 3693, 9236, 4618, 2309, 5776, 2888, 1444, 722, 361, 906, 453, 1136, 568, 284, 142, 71, 181, 456, 228, 114} | Longitud: 42 | Paridad: IPIPIPPIIIPPIIPIPIIPIPIPPIPPPPIPIPPPPIIPPPn = 35 Cycle: {91, 231, 581, 1456, 728, 364, 182} | Length: 7 | Parity: IIIPPPPn = 119 Cycle: {119, 301, 756, 378, 189, 476, 238} | Length: 7 | Parity: IIPPIPP More detailed tables and additional values of r and n can be found in the extended dataset 5n+r. See also a mirror in Link GitHub. All outputs were generated by custom Mathematica code developed specifically for these experiments.

Database and Mathematica code for cycle detection and structural analysis in generalized Collatz systems of the form 3n+r and 5n+r, including cycle lengths, parity sequences, and associated dynamical parameters. https://sites.google.com/view/explorationanid2023/collatz-database Repository structure database-3n+r/ Databases of detected cycles for generalized Collatz maps of the form 3n+r. database-5n+r/ Databases of detected cycles and dynamical behavior for maps of the form 5n+r. code-3n+r.nb Mathematica code used to generate the 3n+r database. code-5n+r.nb Mathematica code used to generate the 5n+r database.