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A322130
Fermat pseudoprimes to base 2 that are hexagonal.
3
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
Andrzej Rotkiewicz, On some problems of W. Sierpinski, Acta Arithmetica, Vol. 21 (1972), pp. 251-259.
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
KEYWORD
nonn
AUTHOR
Amiram Eldar, Nov 27 2018
STATUS
approved