A357907 -id:A357907 - cp's OEIS frontend

A384934 Consecutive states of the linear congruential pseudo-random number generator 254*s mod (2^16+1) when started at s=1.

1, 254, 64516, 2814, 59386, 10534, 54156, 58391, 19952, 21459, 11015, 45256, 26049, 62746, 11993, 31520, 10566, 62284, 25719, 44463, 21238, 20418, 8749, 59525, 45840, 43311, 56315, 16944, 43871, 1944, 35017, 46823, 30845, 35727, 30552, 26842, 2020, 54321

Offset: 1

Sean A. Irvine, Jun 12 2025

Periodic with period 2^16.

Sean A. Irvine, Table of n, a(n) for n = 1..10000
B. D. Ripley, Computer Generation of Random Variables: A Tutorial, International Statistical Review, 51 (1983), 301-309.
W. E. Sharp and Carter Bays, A review of portable random number generators, Computers and Geosciences, 18, 1 (1982), 79-87.
Alan Tootill, PCW Subset, Personal Computer World, June 1982, see p. 133.
Index entries for sequences related to pseudo-random numbers.

Cf. A357907.

NestList[Mod[254*#, 2^16 + 1] &, 1, 50] (* Paolo Xausa, Jun 13 2025 *)

a(n) = 254 * a(n-1) mod (2^16+1).

A384961 Consecutive states of the linear congruential pseudo-random number generator (257*s + 41) mod 2^16 when started at s=1.

Original entry on oeis.org

1, 298, 11091, 32380, 64165, 40910, 28151, 25888, 34121, 52850, 16539, 56260, 40941, 36118, 41791, 57960, 19089, 56250, 38371, 30988, 34101, 47710, 6279, 40880, 20441, 10498, 11051, 22100, 43645, 10150, 52687, 40184, 38177, 46666, 115, 29596, 4037, 54510

Offset: 1

Sean A. Irvine, Jun 13 2025

Periodic with period 2^16.

Sean A. Irvine, Table of n, a(n) for n = 1..10000
B. D. Ripley, Computer Generation of Random Variables: A Tutorial, International Statistical Review, 51 (1983), 301-309.
W. E. Sharp and Carter Bays, A review of portable random number generators, Computers and Geosciences, 18, 1 (1982), 79-87.
Alan Tootill, PCW Subset, Personal Computer World, Feb 1982 (see p. 157).
Index entries for sequences related to pseudo-random numbers.
Index entries for linear recurrences with constant coefficients, order 65536.

Cf. A357907, A384934, A384935.

a:= proc(n) option remember; `if`(n<2, n,
      irem(257*a(n-1)+41, 2^16))
    end:
seq(a(n), n=1..38);  # Alois P. Heinz, Jun 13 2025

NestList[Mod[257*# + 41, 2^16] &, 1, 50] (* Paolo Xausa, Jun 18 2025 *)

a(n) = (257 * a(n-1) + 41) mod 2^16.

cp's OEIS Frontend

A384934 Consecutive states of the linear congruential pseudo-random number generator 254*s mod (2^16+1) when started at s=1.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Formula