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A293625 Generators of Fermat pseudoprimes to base 2 that are square pyramidal numbers: numbers n such that 12n+1, 18n+1 and 36n+1 are all primes. 1
1, 15, 45, 56, 71, 85, 121, 141, 155, 176, 185, 206, 255, 275, 301, 346, 350, 380, 401, 470, 506, 511, 540, 680, 710, 745, 786, 801, 871, 946, 1025, 1156, 1200, 1211, 1326, 1380, 1395, 1421, 1480, 1505, 1515, 1590, 1676, 1696, 1710, 1830, 1941, 2066, 2171 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Rotkiewicz proved that if n is in the sequence then P((2^(2(18n+1))-1)/3) is a square pyramidal Fermat pseudoprime to base 2, where P(k) = k*(k+1)*(2k+1)/6 (A000330).

The generated numbers are terms in A293624. The first term is 256409721410526509996425240557391, the next 2 terms are about 3.683...*10^487 and 8.007...*10^1462.

LINKS

Table of n, a(n) for n=1..49.

Andrzej Rotkiewicz, On pyramidal numbers of order 4, Elemente der Mathematik, Vol. 28 (1973), pp. 14-16.

EXAMPLE

1 is in the sequence since 12*1+1 = 13, 18*1+1 = 19 and 36*1+1 = 37 are all primes. P((2^(2(18*1+1))-1)/3) = P(91625968981) = 256409721410526509996425240557391 is a Fermat pseudoprime to base 2.

MATHEMATICA

Select[Range[1, 1000], PrimeQ[12#+1] && PrimeQ[18#+1] && PrimeQ[36#+1] &]

CROSSREFS

Cf. A000330, A001567, A293624.

Sequence in context: A295980 A029827 A119123 * A084821 A298462 A066763

Adjacent sequences:  A293622 A293623 A293624 * A293626 A293627 A293628

KEYWORD

nonn

AUTHOR

Amiram Eldar, Oct 13 2017

STATUS

approved

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Last modified May 22 00:25 EDT 2019. Contains 323472 sequences. (Running on oeis4.)