A322160 Fermat pseudoprimes to base 2 that are octadecagonal.

8481, 14491, 29341, 62745, 196093, 396271, 526593, 2184571, 2513841, 5256091, 7017193, 8137585, 13448593, 15247621, 16053193, 16879501, 18740971, 20494401, 29878381, 33704101, 35703361, 36724591, 41607721, 42709591, 69741001, 70593931, 80927821, 82976181

Offset

1,1

Comments

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

Intersection of A001567 and A051870.

The corresponding indices of the octadecagonal numbers are 33, 43, 61, 89, 157, 223, 257, 523, 561, 811, 937, 1009, 1297, 1381, 1417, 1453, 1531, ...

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

octadec[n_]:=n(8n-7); Select[octadec[Range[1, 1000]], PowerMod[2, (# - 1), #]==1 &]

Prog

(PARI) isok(n) = (n>1) && ispolygonal(n, 18) && !isprime(n) && (Mod(2, n)^n==2); \\ Michel Marcus, Nov 29 2018

Crossrefs

Cf. A001567, A051870, A293623, A293624, A322161.

Sequence in context: A232907 A151643 A031590 * A253499 A253492 A253453

Adjacent sequences: A322157 A322158 A322159 * A322161 A322162 A322163

Keyword

nonn

Author

Amiram Eldar, Nov 29 2018

Status

approved