A117876 Primes p=prime(k) of level (1,2), i.e., such that A118534(k) = prime(k-2).

23, 47, 73, 233, 353, 647, 1097, 1283, 1433, 1453, 1493, 1613, 1709, 1889, 2099, 2161, 2383, 2621, 2693, 2713, 3049, 3533, 3559, 3923, 4007, 4133, 4643, 4793, 4937, 5443, 5743, 6101, 7213, 7309, 7351, 7561, 7621, 7829, 8179, 8237, 8719, 8849, 9109, 9343, 9467

Offset

1,1

Comments

If prime(k) has level 1 in A117563, and if 2*prime(k) - prime(k+1) = prime(k-i), then we say that prime(k) has level (1,i). Sequence gives primes of level (1,2).

The prime p(4)=7 cannot be decomposed into weight*level+gap (<=> A117563(4)=0 <=> A118534(4)=0 <=> A117078(4)=0). For all other primes, an equivalent definition would be: Primes p(k) such that 2*p(k) - p(k+1) = p(k-2). - Rémi Eismann and M. F. Hasler, Nov 08 2009

Links

Remi Eismann, Table of n, a(n) for n = 1..10000

Formula

a(n) = A000040(A066495(n+1)). - Antti Karttunen, Nov 30 2013

Example

29 = 2*23 - 17, 2179 = 2*2161 - 2143, 5749 = 2*5743 - 5737.

Mathematica

With[{m = 2}, Prime@ Select[Range[m + 1, 1200], If[MemberQ[{1, 2, 4}, #], 0, 2 Prime[#] - Prime[# + 1]] == Prime[# - m] &]] (* Michael De Vlieger, Jul 16 2017 *)

Prog

(PARI) for(n=5, 9999, 2*prime(n)-prime(n+1) == prime(n-2) & print1(prime(n), ", ")) \\ M. F. Hasler, Nov 08 2009
(PARI) is_A117876(p)={ isprime(p) & isprime(d=2*p-nextprime(p+2)) & d == precprime(precprime(p-2)-2) & p>7 } \\ M. F. Hasler, Nov 08 2009
(Scheme) (define (A117876 n) (A000040 (A066495 (+ 1 n)))) ;; Antti Karttunen, Nov 30 2013

Crossrefs

Cf. A000040, A066495, A117078, A117563, A118534.

Sequence in context: A001124 A139501 A292509 * A338386 A090191 A281022

Adjacent sequences: A117873 A117874 A117875 * A117877 A117878 A117879

Keyword

nonn

Author

Rémi Eismann, May 02 2006

Extensions

Edited by N. J. A. Sloane, May 14 2006

More terms from Rémi Eismann, May 25 2006

Definition corrected and terms double-checked by M. F. Hasler, Nov 08 2009

Status

approved