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

Author

Amiram Eldar, Nov 29 2018

Keywords

• nonn

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.

Crossrefs

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

Programs

Mathematica

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

PARI

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