This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A358528 #7 Nov 22 2022 22:20:24 %S A358528 5,11,17,23,29,37,47,53,67,79,89,97,107,113,127,137,149,157,173,191, %T A358528 197,211,233,239,251,277,293,307,317,331,347,353,359,367,389,397,409, %U A358528 419,431,439,449,457,467,479,499,509,521,541,557,577,587,607,631,647 %N A358528 a(n) = n-th prime p(k) such that p(k) - p(k-1) > p(k-1) - p(k-2). %C A358528 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. %e A358528 n 1 2 3 4 5 6 7 %e A358528 k 3 5 7 9 10 12 15 %e A358528 p(n) 5 11 17 23 29 37 47 %t A358528 t = Select[2 + Range[140], %t A358528 Prime[#] - Prime[# - 1] > Prime[# - 1] - Prime[# - 2] &] (* A358529 *) %t A358528 Prime[t] (* A358528 *) %Y A358528 Cf. A358529, A358530, A358531, A181424, A356347. %K A358528 nonn,easy %O A358528 1,1 %A A358528 _Clark Kimberling_, Nov 21 2022