A384113 -id:A384113 - cp's OEIS frontend

A384971 Consecutive internal states of the linear congruential pseudo-random number generator (106*s + 1283) mod 6075 when started at 1.

1, 1389, 2717, 3760, 4968, 5441, 904, 5982, 3575, 3583, 4431, 3194, 5722, 315, 4298, 1246, 5784, 812, 2305, 2613, 4886, 2824, 2952, 4370, 2803, 726, 5339, 2242, 2010, 1718, 1141, 729, 5657, 5575, 2958, 5006, 3394, 2622, 5840, 673, 5796, 2084, 3487, 330, 5888

Offset: 1

Sean A. Irvine, Jun 13 2025

Periodic with period 6075.

Described in Numerical Recipes as a "quick and dirty" generator.

William H. Press, Saul A. Teukolsky, William T. Vetterling, and Brian P. Flannery, Numerical Recipes in C (2nd ed), Cambridge University Press, 1999 (see p. 285).

Sean A. Irvine, Table of n, a(n) for n = 1..6075
W. E. Sharp and Carter Bays, A review of portable random number generators, Computers and Geosciences, 18, 1 (1982), 79-87.
Index entries for sequences related to pseudo-random numbers.
Index entries for linear recurrences with constant coefficients, order 6075.

Cf. A384113, A384114, A384126, A384152, A384158, A384196.

a:= proc(n) option remember; `if`(n<2, n,
      irem(106*a(n-1)+1283, 6075))
    end:
seq(a(n), n=1..45);  # Alois P. Heinz, Jun 13 2025

NestList[Mod[106*# + 1283, 6075] &, 1, 50] (* Paolo Xausa, Jun 17 2025 *)

a(n) = (106*a(n-1) + 1283) mod 6075.

A385002 Consecutive states of the linear congruential pseudo-random number generator (211*s + 1663) mod 7875 when started at s=1.

Original entry on oeis.org

1, 1874, 3327, 2785, 6548, 5166, 4939, 4292, 1650, 3313, 7706, 5379, 2632, 5765, 5328, 7621, 3194, 6222, 7255, 4718, 4911, 6259, 7187, 6120, 1483, 7451, 6699, 5527, 2360, 3498, 7366, 4514, 1242, 3850, 2888, 4656, 7579, 2207, 2715, 7528, 7196, 144, 547, 6830

Offset: 1

Sean A. Irvine, Jun 14 2025

Periodic with period 7875.

Described in Numerical Recipes as a "quick and dirty" generator.

William H. Press, Saul A. Teukolsky, William T. Vetterling, and Brian P. Flannery, Numerical Recipes in C (2nd ed), Cambridge University Press, 1999 (see p. 285).

Sean A. Irvine, Table of n, a(n) for n = 1..7875
W. E. Sharp and Carter Bays, A review of portable random number generators, Computers and Geosciences, 18, 1 (1982), 79-87.
Index entries for sequences related to pseudo-random numbers.
Index entries for linear recurrences with constant coefficients, order 7875.

Cf. A384113, A384971, A385003.

a:= proc(n) option remember; `if`(n<2, n,
      irem(211*a(n-1)+1663, 7875))
    end:
seq(a(n), n=1..44);  # Alois P. Heinz, Jun 14 2025

NestList[Mod[211*# + 1663, 7875] &, 1, 50] (* Paolo Xausa, Jun 17 2025 *)

a(n) = (211 * a(n-1) + 1663) mod 7875.

A385003 Consecutive states of the linear congruential pseudo-random number generator (421*s + 1663) mod 7875 when started at s=1.

Original entry on oeis.org

1, 2084, 4902, 2155, 3293, 2016, 7774, 6392, 7320, 4258, 6656, 339, 2632, 7235, 7848, 6046, 3404, 1497, 1900, 6188, 186, 1219, 2987, 7065, 7153, 4826, 1659, 7102, 6980, 2868, 4216, 4724, 5967, 1645, 1208, 6231, 2539, 7457, 6810, 2173, 2996, 2979, 3697, 6725

Offset: 1

Sean A. Irvine, Jun 14 2025

Periodic with period 7875.

Described in Numerical Recipes as a "quick and dirty" generator.

William H. Press, Saul A. Teukolsky, William T. Vetterling, and Brian P. Flannery, Numerical Recipes in C (2nd ed), Cambridge University Press, 1999 (see p. 285).

Sean A. Irvine, Table of n, a(n) for n = 1..7875
W. E. Sharp and Carter Bays, A review of portable random number generators, Computers and Geosciences, 18, 1 (1982), 79-87.
Index entries for sequences related to pseudo-random numbers.
Index entries for linear recurrences with constant coefficients, order 7875.

Cf. A384113, A384971, A385002.

a:= proc(n) option remember; `if`(n<2, n,
      irem(421*a(n-1)+1663, 7875))
    end:
seq(a(n), n=1..44);  # Alois P. Heinz, Jun 14 2025

NestList[Mod[421*# + 1663, 7875] &, 1, 50] (* Paolo Xausa, Jun 17 2025 *)

a(n) = (421 * a(n-1) + 1663) mod 7875.

A384152 Consecutive states of the linear congruential pseudo-random number generator used by OMNITAB II when started at 1.

Original entry on oeis.org

1, 125, 7433, 3429, 2641, 2445, 2521, 3829, 3489, 1949, 6057, 3461, 6641, 2733, 5753, 6421, 8001, 701, 5705, 421, 3473, 8141, 1817, 5941, 5345, 4573, 6377, 2501, 1329, 2285, 7097, 2389, 3713, 5373, 8073, 1509, 209, 1549, 5209, 3957, 3105, 3101, 2601, 5637, 113

Offset: 1

Sean A. Irvine, May 20 2025

Periodic with period length 2048.
A terrible generator with period much less than the modulus.
Also, RN5 of the IRCCRAND package.
Originally defined by Kruskal including the implementation s = 5*s mod 8192; s = 5*s mod 8192; s = 5*s mod 8192 (rather than s = 125*s mod 8192).

Sean A. Irvine, Table of n, a(n) for n = 1..2048
Edward J. Dudewicz, IRCCRAND - The Ohio State University Random Number Generator Package, Technical Report, 1974.
David Hogben, Sally T. Peavy, and Ruth N. Varner, OMNITAB II: User's Reference Manual, NBS Technical Note 552, 1971.
J. B. Kruskal, Extremely portable random number generator, Communications of the ACM, 12, 2 (1969), 93-94.
W. E. Sharp and Carter Bays, A review of portable random number generators, Computers and Geosciences, 18, 1 (1982), 79-87.
Index entries for sequences related to pseudo-random numbers.
Index entries for linear recurrences with constant coefficients, order 2048.

Cf. A096550-A096561 (other pseudo-random number generators).

Cf. A383809, A384113, A384126, A384971, A384973 (other examples with short periods).

a:= proc(n) option remember; `if`(n<2, n,
      irem(125*a(n-1), 2^13))
    end:
seq(a(n), n=1..45);  # Alois P. Heinz, May 21 2025

NestList[Mod[125*#, 2^13] &, 1, 100] (* Paolo Xausa, May 21 2025 *)

a(n) = lift(Mod(5,8192)^(3*n-3)) \\ Jianing Song, Jul 06 2025

a(n) = 125 * a(n-1) mod 2^13.

A385036 Consecutive states of the linear congruential pseudo-random number generator (419*s + 6173) mod 29282 when started at s=1.

Original entry on oeis.org

1, 6592, 15713, 1470, 7181, 28248, 12157, 4888, 4505, 19720, 11329, 9340, 25127, 22148, 3791, 13374, 17017, 20770, 12049, 18200, 18653, 3486, 2707, 27690, 12611, 19422, 3595, 19096, 13411, 3238, 15923, 1614, 8953, 9384, 14281, 16384, 19081, 7126, 5203, 19362

Offset: 1

Sean A. Irvine, Jun 16 2025

Periodic with period 29282.

Described in Numerical Recipes as a "quick and dirty" generator.

William H. Press, Saul A. Teukolsky, William T. Vetterling, and Brian P. Flannery, Numerical Recipes in C (2nd ed), Cambridge University Press, 1999 (see p. 285).

Sean A. Irvine, Table of n, a(n) for n = 1..10000
W. E. Sharp and Carter Bays, A review of portable random number generators, Computers and Geosciences, 18, 1 (1982), 79-87.
Index entries for sequences related to pseudo-random numbers.
Index entries for linear recurrences with constant coefficients, order 29282.

Cf. A384113, A384971, A385002.

a:= proc(n) option remember; `if`(n<2, n,
      irem(419*a(n-1)+6173, 29282))
    end:
seq(a(n), n=1..44);  # after Alois P. Heinz

NestList[Mod[419*# + 6173, 29282] &, 1, 50] (* Paolo Xausa, Jun 17 2025 *)

a(n) = (419 * a(n-1) + 6173) mod 29282.

A385039 Consecutive internal states of the linear congruential pseudo-random number generator (171*s + 11213) mod 53125 when started at 1.

Original entry on oeis.org

1, 11384, 45377, 14430, 34993, 45016, 5824, 50867, 50095, 24333, 28406, 34264, 26607, 45385, 15798, 3296, 43579, 25722, 300, 9388, 22811, 33769, 48212, 21090, 5103, 33826, 4834, 40952, 1505, 2943, 36341, 9899, 3942, 47795, 2908, 30356, 48964, 43432, 585, 4998

Offset: 1

Sean A. Irvine, Jun 13 2025

Periodic with period 53125.

Described in Numerical Recipes as a "quick and dirty" generator.

William H. Press, Saul A. Teukolsky, William T. Vetterling, and Brian P. Flannery, Numerical Recipes in C (2nd ed), Cambridge University Press, 1999 (see p. 285).

Sean A. Irvine, Table of n, a(n) for n = 1..10000
W. E. Sharp and Carter Bays, A review of portable random number generators, Computers and Geosciences, 18, 1 (1982), 79-87.
Index entries for sequences related to pseudo-random numbers.
Index entries for linear recurrences with constant coefficients, order 53125.

Cf. A384113, A384114, A384126, A384152, A384158, A384196.

a:= proc(n) option remember; `if`(n<2, n,
      irem(171*a(n-1)+11213, 53125))
    end:
seq(a(n), n=1..45);  # after Alois P. Heinz

NestList[Mod[171*# + 11213, 53125] &, 1, 50] (* Paolo Xausa, Jun 16 2025 *)

a(n) = (171*a(n-1) + 11213) mod 53125.

A385078 Consecutive states of the linear congruential pseudo-random number generator (967*s + 3041) mod 14406 when started at s=1.

Original entry on oeis.org

1, 4008, 3563, 5428, 8133, 1976, 12241, 12762, 12359, 11620, 2901, 13544, 5035, 2658, 9059, 4246, 3213, 12722, 2491, 6036, 5423, 3298, 8481, 7154, 6079, 3786, 4979, 6130, 9885, 10658, 9037, 11784, 3023, 1864, 4779, 8, 10777, 8862, 1025, 202, 11097, 1370, 2479

Offset: 1

Sean A. Irvine, Jun 16 2025

Periodic with period 14406.

Described in Numerical Recipes as a "quick and dirty" generator.

William H. Press, Saul A. Teukolsky, William T. Vetterling, and Brian P. Flannery, Numerical Recipes in C (2nd ed), Cambridge University Press, 1999 (see p. 285).

Sean A. Irvine, Table of n, a(n) for n = 1..14406
W. E. Sharp and Carter Bays, A review of portable random number generators, Computers and Geosciences, 18, 1 (1982), 79-87.
Index entries for sequences related to pseudo-random numbers.
Index entries for linear recurrences with constant coefficients, order 14406.

Cf. A384113, A384971, A385002, A385036.

a:= proc(n) option remember; `if`(n<2, n,
      irem(967*a(n-1)+3041, 14406))
    end:
seq(a(n), n=1..44);  # after Alois P. Heinz

NestList[Mod[967*# + 3041, 14406] &, 1, 50] (* Paolo Xausa, Jun 17 2025 *)

a(n) = (967 * a(n-1) + 3041) mod 14406.

A385037 Consecutive states of the linear congruential pseudo-random number generator (936*s + 1399) mod 6655 when started at s=1.

Original entry on oeis.org

1, 2335, 4119, 3538, 5432, 1331, 2730, 1159, 1458, 1812, 406, 2080, 5019, 753, 777, 3276, 6435, 1784, 818, 1722, 2681, 1880, 4159, 1048, 4042, 4671, 1120, 4884, 838, 477, 1986, 3550, 3354, 6238, 3732, 676, 1910, 5619, 3333, 6547, 136, 2250, 4419, 4828, 1662

Offset: 1

Sean A. Irvine, Jun 14 2025

Periodic with period 6655.

Described in Numerical Recipes as a "quick and dirty" generator.

William H. Press, Saul A. Teukolsky, William T. Vetterling, and Brian P. Flannery, Numerical Recipes in C (2nd ed), Cambridge University Press, 1999 (see p. 285).

Sean A. Irvine, Table of n, a(n) for n = 1..6655
W. E. Sharp and Carter Bays, A review of portable random number generators, Computers and Geosciences, 18, 1 (1982), 79-87.
Index entries for sequences related to pseudo-random numbers.
Index entries for linear recurrences with constant coefficients, order 6655.

Cf. A384113, A384971, A385002, A385003.

a:= proc(n) option remember; `if`(n<2, n,
      irem(936*a(n-1)+1399, 6655))
    end:
seq(a(n), n=1..44);  # after Alois P. Heinz

NestList[Mod[936*# + 1399, 6655] &, 1, 50] (* Paolo Xausa, Jun 16 2025 *)

a(n) = (936 * a(n-1) + 1399) mod 6655.

A385079 Consecutive states of the linear congruential pseudo-random number generator 228*s mod (2^16+1) when started at s=1.

Original entry on oeis.org

1, 228, 51984, 55692, 49135, 61490, 60339, 60059, 61756, 55450, 59496, 64466, 17960, 31586, 58075, 2626, 8895, 61950, 34145, 51694, 55109, 47285, 32912, 32718, 54023, 61825, 5645, 41857, 40531, 351, 14491, 27098, 17866, 10154, 21317, 10538, 43332, 49146, 63998

Offset: 1

Sean A. Irvine, Jun 16 2025

Periodic with period 2^16.

Attributed by Sharp and Bays to L. Afflerbach.

Sean A. Irvine, Table of n, a(n) for n = 1..10000
W. E. Sharp and Carter Bays, A review of portable random number generators, Computers and Geosciences, 18, 1 (1982), 79-87.
Index entries for sequences related to pseudo-random numbers.
Index entries for linear recurrences with constant coefficients, order 65536.

Cf. A384113, A384971, A385002, A385080.

a:= proc(n) option remember; `if`(n<2, n,
      irem(228*a(n-1), 65537))
    end:
seq(a(n), n=1..44);  # after Alois P. Heinz

NestList[Mod[228*#, 65537] &, 1, 50] (* Paolo Xausa, Jun 17 2025 *)

a(n) = lift(Mod(228, 65537)^(n-1)) \\ Jianing Song, Jun 17 2025

a(n) = 228 * a(n-1) mod (2^16+1).

A385038 Consecutive internal states of the linear congruential pseudo-random number generator (1366*s + 1283) mod 6075 when started at 1.

Original entry on oeis.org

1, 2649, 5192, 4030, 2313, 1841, 1039, 5082, 5645, 3178, 4881, 4454, 4372, 1710, 4343, 4621, 1644, 5312, 3925, 4683, 1286, 2284, 4752, 4415, 5773, 1851, 2549, 2242, 2055, 1763, 3841, 5364, 2057, 4495, 5703, 3431, 4204, 3072, 5885, 2968, 3546, 3344, 787, 1050

Offset: 1

Sean A. Irvine, Jun 13 2025

Periodic with period 6075.

Described in Numerical Recipes as a "quick and dirty" generator.

William H. Press, Saul A. Teukolsky, William T. Vetterling, and Brian P. Flannery, Numerical Recipes in C (2nd ed), Cambridge University Press, 1999 (see p. 285).

Sean A. Irvine, Table of n, a(n) for n = 1..6075
W. E. Sharp and Carter Bays, A review of portable random number generators, Computers and Geosciences, 18, 1 (1982), 79-87.
Index entries for sequences related to pseudo-random numbers.

Cf. A384113, A384114, A384126, A384152, A384158, A384196, A384971, A385037.

a:= proc(n) option remember; `if`(n<2, n,
      irem(1366*a(n-1)+1283, 6075))
    end:
seq(a(n), n=1..45);  # after Alois P. Heinz

NestList[Mod[1366*# + 1283, 6075] &, 1, 50] (* Paolo Xausa, Jun 16 2025 *)

a(n) = (1366*a(n-1) + 1283) mod 6075.

cp's OEIS Frontend

A384971 Consecutive internal states of the linear congruential pseudo-random number generator (106*s + 1283) mod 6075 when started at 1.

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A385002 Consecutive states of the linear congruential pseudo-random number generator (211*s + 1663) mod 7875 when started at s=1.

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A385003 Consecutive states of the linear congruential pseudo-random number generator (421*s + 1663) mod 7875 when started at s=1.

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A384152 Consecutive states of the linear congruential pseudo-random number generator used by OMNITAB II when started at 1.

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A385036 Consecutive states of the linear congruential pseudo-random number generator (419*s + 6173) mod 29282 when started at s=1.

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A385039 Consecutive internal states of the linear congruential pseudo-random number generator (171*s + 11213) mod 53125 when started at 1.

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A385078 Consecutive states of the linear congruential pseudo-random number generator (967*s + 3041) mod 14406 when started at s=1.

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