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

Author

Rémi Eismann, May 02 2006

Keywords

• nonn

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

Examples

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

Links

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

Crossrefs

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

Programs

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 *)

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

Formula

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

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