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A214607 Fermat pseudoprimes to base 2 of the form (6*k + 1)*(6*k*n + 1), where k, n are integers different from 0. 0
1105, 1387, 1729, 2701, 2821, 4033, 4681, 5461, 6601, 8911, 10261, 10585, 11305, 13741, 13981, 14491, 15841, 16705, 18721, 29341, 30121, 30889, 31609, 31621, 39865, 41041, 41665, 46657, 49141, 52633, 57421, 63973, 65281, 68101, 75361 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

These are also called Poulet numbers. A few examples of how the formula looks like for k and n from 1 to 4:

For k = 1 the formula becomes 42*n + 7.

For k = 2 the formula becomes 156*n + 13.

For k = 3 the formula becomes 342*n + 19.

For k = 4 the formula becomes 600*n + 25.

For n = 1 the formula generates a perfect square.

For n = 2 the formula becomes (6*k + 1)*(12*k + 1) and were found the following Poulet numbers: 2701, 8911, 10585, 18721, 49141 etc.

For n = 3 the formula becomes (6*k + 1)*(18*k + 1) and were found the following Poulet numbers: 2821, 4033, 5461, 15841, 31621, 68101, etc.

For n = 4 the formula becomes (6*k + 1)*(24*k + 1). See the sequence A182123.

Note: the formula is equivalent to Poulet numbers of the form p*(n*p - n + 1), where p is of the form 6*k + 1. From the first 68 Poulet numbers just 7 of them (7957, 23377, 33153, 35333, 42799, 49981, 60787) can't be written as p*(n*p - n + 1), where p is of the form 6*k +- 1 and k, n are integers different from 0.

LINKS

Table of n, a(n) for n=1..35.

Eric Weisstein's World of Mathematics, Poulet Number

MATHEMATICA

t = Select[Union[Flatten[Table[(6*k + 1)*(6*k*n + 1), {k, 100}, {n, 2000}]]], # < 76000 &]; Select[t, PowerMod[2, #, #] == 2 &] (* T. D. Noe, Jul 24 2012 *)

CROSSREFS

Cf. A001567, A182123.

Sequence in context: A107519 A168629 A175521 * A321870 A257759 A025295

Adjacent sequences:  A214604 A214605 A214606 * A214608 A214609 A214610

KEYWORD

nonn

AUTHOR

Marius Coman, Jul 22 2012

STATUS

approved

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Last modified October 18 02:23 EDT 2019. Contains 328135 sequences. (Running on oeis4.)