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 A117876 Primes p=prime(k) of level (1,2), i.e., such that A118534(k) = prime(k-2). 19
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Let prime(i) denote the i-th prime. If prime(n) has level 1 in A117563, and if 2 prime(n) - prime(n+1) is a prime, say prime(n-i), then we say that prime(n) 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(n) such that 2*p(n) - p(n+1) = p(n-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 * A090191 A281022 A054821 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

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Last modified December 17 06:45 EST 2018. Contains 318192 sequences. (Running on oeis4.)