%I #23 Jun 19 2021 04:01:06

%S 15823,21617,31277,43331,65731,97883,100853,120947,265277,318023,

%T 320953,361241,362759,419831,422141,426799,452549,465211,482441,

%U 491539,504403,513533,526781,540391,551597,557093,575261,582251,598729,649093,654629,663601,678779,782723

%N Primes p=prime(i) of level (1,6), i.e., such that A118534(i) = prime(i-6).

%C If prime(i) has level 1 in A117563 and 2*prime(i) - prime(i+1) = prime(i-k), then we say that prime(i) has level (1,k).

%H Fabien Sibenaler, <a href="/A216180/b216180.txt">Table of n, a(n) for n = 1..10000</a>

%e 31277 = prime(3373) is a term because 2*prime(3373) - prime(3374) = 2*31277 - 31307 = 31247 = prime(3367).

%t With[{m = 6}, Prime@ Select[Range[m + 1, 5*10^4], If[MemberQ[{1, 2, 4}, #], 0, 2 Prime[#] - Prime[# + 1]] == Prime[# - m] &]] (* _Michael De Vlieger_, Jul 16 2017 *)

%o (PARI) lista(nn) = my(c=7, v=primes(7)); forprime(p=19, nn, if(2*v[c]-p==v[c=c%7+1], print1(precprime(p-1), ", ")); v[c]=p); \\ _Jinyuan Wang_, Jun 18 2021

%Y Subsequence of A125830 and of A162174.

%Y Cf. A117078, A117563, A006562 (primes of level (1,1)), A117876, A118464, A118467, A119402, A119403, A119404, A125565, A125572, A125574, A125576, A125623.

%K nonn

%O 1,1

%A _Fabien Sibenaler_, Mar 10 2013