A064051 a(n) = 2*prime(n)^2 - prime(n+1)^2.

-1, -7, 1, -23, 73, 49, 217, 193, 217, 721, 553, 1057, 1513, 1489, 1609, 2137, 3241, 2953, 3937, 4753, 4417, 5593, 5857, 6433, 8617, 9793, 9769, 11017, 10993, 9409, 15097, 15553, 18217, 16441, 21601, 20953, 22729, 25249, 25849, 27817, 31321, 29041, 35713

Offset

1,2

Comments

Theorem: a(n) > 0 for all n > 4.

References

D. S. Mitrinovic et al., Handbook of Number Theory, Kluwer, 1996, Section VII.18, p. 247.

Links

Harry J. Smith, Table of n, a(n) for n = 1..1000

Formula

a(n) = 2*A001248(n) - A001248(n+1). - Elmo R. Oliveira, Jan 13 2023

Mathematica

Table[2 Prime[n]^2 - Prime[n+1]^2, {n, 45}] (* Vincenzo Librandi, Jun 22 2018 *)
2#[[1]]-#[[2]]&/@Partition[Prime[Range[50]]^2, 2, 1] (* Harvey P. Dale, May 15 2023 *)

Prog

(PARI) a(n) = 2*prime(n)^2 - prime(n + 1)^2; \\ Harry J. Smith, Sep 06 2009
(Magma) [2*NthPrime(n)^2 - NthPrime(n+1)^2: n in [1..45]]; // Vincenzo Librandi, Jun 22 2018

Crossrefs

Cf. A324798, A001248.

Sequence in context: A261248 A214686 A211790 * A147385 A147347 A183109

Adjacent sequences: A064048 A064049 A064050 * A064052 A064053 A064054

Keyword

sign

Author

N. J. A. Sloane, Oct 15 2001

Status

approved