A272934 -id:A272934 - cp's OEIS frontend

A289382 a(n) = 2^n mod triangular(n).

0, 1, 2, 6, 2, 1, 16, 4, 17, 34, 2, 40, 2, 4, 8, 120, 104, 1, 78, 46, 134, 70, 140, 16, 132, 121, 134, 30, 2, 94, 64, 400, 206, 429, 158, 334, 2, 4, 8, 616, 494, 1, 690, 346, 692, 142, 848, 64, 912, 1024, 8, 796, 797, 379, 1528, 4, 350, 178, 1418, 916, 2, 4, 512, 1056, 32, 2011

Offset: 1

Alex Ratushnyak, Jul 04 2017

nonn

			a(6) = 2**6 mod (6*7/2) = 64 mod 21 = 1.

Seiichi Manyama, Table of n, a(n) for n = 1..10000

Cf. A000079, A000217, A066606, A272934.

seq(2^n mod n*(n+1)/2, n=1..100); # Robert Israel, Jul 04 2017

Table[Mod[2^n, n (n + 1)/2], {n, 66}] (* Michael De Vlieger, Jul 04 2017 *)
PowerMod[2,#,(#(#+1))/2]&/@Range[70] (* Harvey P. Dale, Oct 12 2018 *)

a(n) = lift(Mod(2, n*(n+1)/2)^n); \\ Michel Marcus, Jul 04 2017

for n in range(1,99): print(str(int(2**n % (n*(n+1)/2))), end=', ')

a(n) = A000079(n) mod A000217(n) = 2^n mod n*(n+1)/2.

a(n) = 1 for n>1 in A272934. - Michel Marcus, Jul 04 2017

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

Original entry on oeis.org

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

Juri-Stepan Gerasimov, Aug 29 2024

nonn

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

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

Supersequence of A216822, A217465, A217466 and A375792.

Cf. A000217, A272934, A289382.

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

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

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

cp's OEIS Frontend

A289382 a(n) = 2^n mod triangular(n).

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