A375793 Numbers m such that 2^m == 2 (mod m-th triangular number).

1, 3, 5, 11, 13, 29, 37, 61, 73, 131, 157, 181, 193, 277, 313, 397, 421, 457, 541, 561, 613, 661, 673, 733, 757, 877, 997, 1093, 1153, 1201, 1213, 1237, 1289, 1321, 1381, 1453, 1621, 1657, 1753, 1873, 1905, 1933, 1993, 2017, 2137, 2341, 2473, 2557, 2593, 2797, 2857, 2917, 3061, 3217, 3253, 3313, 3389, 3457

Offset

1,2

Comments

a(19) = 561 is the first composite term of the sequence.

Links

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Maple

t:= n-> n*(n+1)/2:
q:= m-> is(2&^m-2 mod t(m)=0):
select(q, [$1..3457])[];  # Alois P. Heinz, Sep 21 2024

Mathematica

Select[Range[3457], Mod[2^#-2, #(#+1)/2 ]==0&] (* James C. McMahon, Sep 23 2024 *)

Prog

(Magma) [1] cat [m: m in [2..3500] | Modexp(2, m, m*(m+1) div 2) eq 2];

Crossrefs

Supersequence of A216822, A217465, A217466 and A375792.

Cf. A000217, A272934, A289382.

Sequence in context: A287940 A237349 A095082 * A265396 A216553 A250298

Adjacent sequences: A375790 A375791 A375792 * A375794 A375795 A375796

Keyword

nonn

Author

Juri-Stepan Gerasimov, Aug 29 2024

Status

approved