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A106483 Primes p such that 2p^2 - 1 is also prime. 20
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 (list; graph; refs; listen; history; text; internal format)
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 k-th 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)^2-1 is also prime.

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] &] (*Chandler*)

PROG

(MAGMA) [p: p in PrimesUpTo(2500)|  IsPrime(2*p^2-1)] // Vincenzo Librandi, Jan 29 2011

CROSSREFS

Cf. A000040, A001358, A007588, A106482, A106484.

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

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Last modified June 25 04:25 EDT 2019. Contains 324346 sequences. (Running on oeis4.)