A117876 - OEIS

%I #34 Jun 19 2021 02:35:35

%S 23,47,73,233,353,647,1097,1283,1433,1453,1493,1613,1709,1889,2099,

%T 2161,2383,2621,2693,2713,3049,3533,3559,3923,4007,4133,4643,4793,

%U 4937,5443,5743,6101,7213,7309,7351,7561,7621,7829,8179,8237,8719,8849,9109,9343,9467

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

%C 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).

%C 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

%H Remi Eismann, <a href="/A117876/b117876.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A000040(A066495(n+1)). - _Antti Karttunen_, Nov 30 2013

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

%t 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 *)

%o (PARI) for(n=5,9999, 2*prime(n)-prime(n+1) == prime(n-2) & print1(prime(n),",")) \\ _M. F. Hasler_, Nov 08 2009

%o (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

%o (Scheme) (define (A117876 n) (A000040 (A066495 (+ 1 n)))) ;; _Antti Karttunen_, Nov 30 2013

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

%K nonn

%O 1,1

%A _Rémi Eismann_, May 02 2006

%E Edited by _N. J. A. Sloane_, May 14 2006

%E More terms from _Rémi Eismann_, May 25 2006

%E Definition corrected and terms double-checked by _M. F. Hasler_, Nov 08 2009