A321868 Fermat pseudoprimes to base 2 that are octagonal.

341, 645, 2465, 2821, 4033, 5461, 8321, 15841, 25761, 31621, 68101, 83333, 162401, 219781, 282133, 348161, 530881, 587861, 653333, 710533, 722261, 997633, 1053761, 1082401, 1193221, 1246785, 1333333, 1357441, 1398101, 1489665, 1584133, 1690501, 1735841

Offset

1,1

Comments

Rotkiewicz proved that under Schinzel's Hypothesis H this sequence is infinite.

Intersection of A001567 and A000567.

The corresponding indices of the octagonal numbers are 11, 15, 29, 31, 37, 43, 53, 73, 93, 103, 151, 167, 233, 271, 307, 341, 421, 443, 467, 487, 491, 577, 593, 601, 631, 645, 667, 673, 683, 705, 727, 751, 761, 901, 911, 919, 991, ...

First differs from A216170 at n = 505.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Andrzej Rotkiewicz, On some problems of W. Sierpinski, Acta Arithmetica, Vol. 21 (1972), pp. 251-259.

Wikipedia, Schinzel's Hypothesis H.

Mathematica

oct[n_]:=n(3n-2); Select[oct[Range[1, 1000]], PowerMod[2, (# - 1), #]==1 &]

Prog

(PARI) isok(n) = (n>1) && ispolygonal(n, 8) && !isprime(n) && (Mod(2, n)^n==2); \\ Daniel Suteu, Nov 29 2018

Crossrefs

Cf. A000567, A001567, A216170, A293623, A293624, A321869.

Sequence in context: A215326 A153508 A216170 * A175736 A179839 A172255

Adjacent sequences: A321865 A321866 A321867 * A321869 A321870 A321871

Keyword

nonn

Author

Amiram Eldar, Nov 20 2018

Status

approved