A358528 a(n) = n-th prime p(k) such that p(k) - p(k-1) > p(k-1) - p(k-2).

5, 11, 17, 23, 29, 37, 47, 53, 67, 79, 89, 97, 107, 113, 127, 137, 149, 157, 173, 191, 197, 211, 233, 239, 251, 277, 293, 307, 317, 331, 347, 353, 359, 367, 389, 397, 409, 419, 431, 439, 449, 457, 467, 479, 499, 509, 521, 541, 557, 577, 587, 607, 631, 647

Offset: 1

Author

Clark Kimberling, Nov 21 2022

Keywords

• nonn
• easy

Comments

This sequence, together with A358530 and A181424, partition the set of primes >= 5. The corresponding sequences of indices, A358529, A358531, and A356347, partition the set of positive integers >= 3.

Examples

			   n      1   2   3   4   5   6   7
   k      3   5   7   9  10  12  15
   p(n)   5  11  17  23  29  37  47
		

Crossrefs

Cf. A358529, A358530, A358531, A181424, A356347.

Programs

Mathematica

t = Select[2 + Range[140],
Prime[#] - Prime[# - 1] > Prime[# - 1] - Prime[# - 2] &]  (* A358529 *)
Prime[t]  (* A358528 *)