A358530 a(n) = n-th prime prime(k) such that prime(k) - prime(k-1) < prime(k-1) - prime(k-2).

13, 19, 31, 41, 43, 61, 71, 73, 83, 101, 103, 109, 131, 139, 151, 167, 181, 193, 199, 227, 229, 241, 257, 271, 281, 283, 311, 313, 337, 349, 373, 383, 401, 421, 433, 443, 461, 463, 487, 491, 503, 523, 547, 563, 571, 593, 601, 617, 619, 641, 643, 661, 677

Offset: 1

Author

Clark Kimberling, Nov 21 2022

Keywords

• nonn
• easy

Comments

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.

Examples

			  n           1   2   3   4   5   6   7
  k           6   8  11  13  14  18  20
  prime(n)   13  19  31  41  43  61  71
		

Crossrefs

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

Programs

Mathematica

t = Select[2 + Range[140],
Prime[#] - Prime[# - 1] < Prime[# - 1] - Prime[# - 2] &]  (* A358531 *)
Prime[t]  (* A358530 *)

Formula

a(n) = A151800(A051634(n)). - Andrew Howroyd, Sep 21 2024

Extensions

Incorrect formula removed by Georg Fischer, Sep 21 2024