A322123 Fermat pseudoprimes to base 2 that are tetradecagonal.

31609, 60701, 458989, 513629, 679729, 729061, 745889, 1207361, 1994689, 2746589, 4361389, 4974971, 5173601, 5444489, 6749021, 9056501, 12659989, 13295281, 15525241, 15757741, 16070429, 16705021, 20770621, 21400481, 23822329, 23966011, 27492581, 34003061

Offset: 1

Author

Amiram Eldar, Nov 27 2018

Keywords

• nonn

Comments

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

Intersection of A001567 and A051866.

The corresponding indices of the tetradecagonal numbers are 73, 101, 277, 293, 337, 349, 353, 449, 577, 677, 853, 911, 929, 953, 1061, 1229, 1453, 1489, 1609, 1621, 1637, 1669, 1861, 1889, 1993, 1999, ...

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harvey P. Dale)
• Andrzej Rotkiewicz, On some problems of W. Sierpinski, Acta Arithmetica, Vol. 21 (1972), pp. 251-259.
• Wikipedia, Schinzel's Hypothesis H.

Crossrefs

Cf. A001567, A051866, A293623, A293624, A322124.

Programs

Mathematica

tetradec[n_] := n(6n-5); Select[tetradec[Range[1, 1000]], PowerMod[2, (# - 1), #]==1 &]
Select[PolygonalNumber[14,Range[2400]],PowerMod[2,#-1,#]==1&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Dec 11 2018 *)

PARI

isok(n) = ispolygonal(n, 14) && (Mod(2, n)^n==2) && !isprime(n) && (n>1); \\ Michel Marcus, Nov 28 2018