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%I #10 Nov 22 2022 22:20:50
%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 p(k) such that p(k) - p(k-1) < p(k-1) - p(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) = A051634(n) + 2.
%e n 1 2 3 4 5 6 7
%e k 6 8 11 13 14 18 20
%e p(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
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