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a(n) is the least prime(k+n-1) satisfying k > 0 and prime(k+n-1) < prime(k) + prime(k+1).
1

%I #21 Mar 17 2019 04:09:36

%S 7,17,23,41,47,59,67,73,83,103,107,109,137,151,167,179,181,193,197,

%T 233,239,251,257,271,281,283,313,317,349,359,379,383,409,421,431,433,

%U 443,449,467,491,503,523,571,587,593,599,607,613,617,643,647,659,661,677,683,733,739

%N a(n) is the least prime(k+n-1) satisfying k > 0 and prime(k+n-1) < prime(k) + prime(k+1).

%H Seiichi Manyama, <a href="/A322669/b322669.txt">Table of n, a(n) for n = 3..10000</a>

%t Array[Block[{k = 1, p}, While[Set[p, Prime[k + # - 1]] >= Total@ Prime@ {k, k + 1}, k++]; p] &, 57, 3] (* _Michael De Vlieger_, Jan 01 2019 *)

%o (PARI) a(n) = {my(p=2, k=1); while(!(prime(k+n-1) < p+nextprime(p+1)), p = nextprime(p+1); k++); prime(k+n-1);} \\ _Michel Marcus_, Dec 23 2018

%Y Cf. A322668.

%K nonn

%O 3,1

%A _Seiichi Manyama_, Dec 23 2018