A358530 - OEIS

%I #18 Sep 22 2024 02:29:48

%S 13,19,31,41,43,61,71,73,83,101,103,109,131,139,151,167,181,193,199,

%T 227,229,241,257,271,281,283,311,313,337,349,373,383,401,421,433,443,

%U 461,463,487,491,503,523,547,563,571,593,601,617,619,641,643,661,677

%N a(n) = n-th prime prime(k) such that prime(k) - prime(k-1) < prime(k-1) - prime(k-2).

%C This sequence, together with A358528 and A181424, partition the set of primes >= 5. The corresponding sequences of indices, A358531, A358529, and A356347, partition the set of positive integers >= 3.

%F a(n) = A151800(A051634(n)). - _Andrew Howroyd_, Sep 21 2024

%e   n           1   2   3   4   5   6   7

%e   k           6   8  11  13  14  18  20

%e   prime(n)   13  19  31  41  43  61  71

%t t = Select[2 + Range[140],

%t Prime[#] - Prime[# - 1] < Prime[# - 1] - Prime[# - 2] &]  (* A358531 *)

%t Prime[t]  (* A358530 *)

%Y Cf. A001223, A051634, A079419, A358528, A358529, A358531, A181424, A356347.

%K nonn,easy

%O 1,1

%A _Clark Kimberling_, Nov 21 2022

%E Incorrect formula removed by _Georg Fischer_, Sep 21 2024