

A106483


Primes p such that 2p^2  1 is also prime.


22



2, 3, 7, 11, 13, 17, 41, 43, 59, 73, 109, 113, 127, 137, 157, 179, 181, 197, 199, 211, 251, 263, 277, 293, 311, 353, 367, 379, 409, 419, 433, 487, 563, 571, 577, 617, 619, 659, 701, 739, 743, 757, 797, 811, 827, 829, 839, 857, 937, 941, 1009, 1039, 1063
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OFFSET

1,1


COMMENTS

Previous name: Indices of semiprime Stella Octangula numbers A007588.
Because of the polynomial factorization, the Stella Octangula numbers 2*k^2  1 can never be prime. They are semiprime when k is prime and 2*k^2  1 is also prime. That is, the kth Stella Octangula number is semiprime for k = 2, 3, 7, 11, 13, 17, 41, 43, 59, 73, 109, 113, 127, 137, 157, 179, 181, 197, 199, ....


LINKS

T. D. Noe, Table of n, a(n) for n = 1..1000
J. V. Post, Table of Polytope Numbers, Sorted, Through 1,000,000
Eric Weisstein's World of Mathematics, Stella Octangula Number


FORMULA

a(n) is in this sequence iff A007588(a(n))) is an element of A001358. a(n) is in this sequence iff A106482(a(n)) = 2. a(n) is in this sequence iff a(n) is prime and 2*a(n)^21 is also prime.
a(n) = prime(A092058(n)).  R. J. Mathar, Aug 20 2019


EXAMPLE

73 is in this sequence because the 73rd Stella Octangula number = 73*(2*73^2  1) = 777961 = 73 * 10657, which is semiprime.


MATHEMATICA

Select[Table[Prime[n], {n, 500}], PrimeQ[2*#^2  1] &] (* Ray Chandler, May 03 2005 *)


PROG

(MAGMA) [p: p in PrimesUpTo(2500) IsPrime(2*p^21)] // Vincenzo Librandi, Jan 29 2011


CROSSREFS

Cf. A000040, A001358, A007588, A106482, A106484, A177104 (2p^31 prime), A182785 (2p^41 prime)
Cf. A092057 (2p^2  1).
Sequence in context: A023221 A127430 A171595 * A145673 A321657 A040116
Adjacent sequences: A106480 A106481 A106482 * A106484 A106485 A106486


KEYWORD

easy,nonn


AUTHOR

Jonathan Vos Post, May 03 2005


EXTENSIONS

Extended by Ray Chandler, May 03 2005


STATUS

approved



