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

1,3

Links

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

Formula

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

Example

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

Maple

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

Mathematica

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 *)

Prog

(Python)
for n in range(1, 99): print(str(int(2**n % (n*(n+1)/2))), end=', ')
(PARI) a(n) = lift(Mod(2, n*(n+1)/2)^n); \\ Michel Marcus, Jul 04 2017

Crossrefs

Cf. A000079, A000217, A066606, A272934.

Sequence in context: A136760 A303335 A332390 * A062539 A064136 A347238

Adjacent sequences: A289379 A289380 A289381 * A289383 A289384 A289385

Keyword

nonn

Author

Alex Ratushnyak, Jul 04 2017

Status

approved