A322130 Fermat pseudoprimes to base 2 that are hexagonal.

561, 2701, 4371, 8911, 10585, 18721, 33153, 49141, 93961, 104653, 115921, 157641, 226801, 289941, 314821, 334153, 534061, 665281, 721801, 831405, 873181, 915981, 1004653, 1373653, 1537381, 1755001, 1815465, 1987021, 2035153, 2233441, 2284453, 3059101, 3363121

Offset

1,1

Comments

Rotkiewicz proved that under Schinzel's Hypothesis H this sequence is infinite. His proof is the same as that of triangular pseudoprimes, since all the triangular numbers that he generates are also hexagonal (see comment in A320599).

Intersection of A001567 and A000384.

Subsequence of A293622.

The corresponding indices of the hexagonal numbers are 17, 37, 47, 67, 73, 97, 129, 157, 217, 229, 241, 281, 337, 381, 397, 409, 517, 577, 601, 645, 661, 677, 709, 829, 877, 937, 953, 997, ...

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

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

Prog

(PARI) isok(n) = ispolygonal(n, 6) && (Mod(2, n)^n==2) && !isprime(n) && (n>1); \\ Michel Marcus, Nov 28 2018

Crossrefs

Cf. A000384, A001567, A293622, A293623, A293624, A320599.

Sequence in context: A205947 A290692 A293622 * A354609 A207080 A339875

Adjacent sequences: A322127 A322128 A322129 * A322131 A322132 A322133

Keyword

nonn

Author

Amiram Eldar, Nov 27 2018

Status

approved