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 A075275 #17 Jan 20 2025 15:18:37
%S A075275 5,7,10,11,22,41,67,76,91,96,163,245,299,341,434,510,535,800,935,1401,
%T A075275 1403,1747
%N A075275 Numbers k such that k!! is an interprime, i.e., the average of two successive primes.
%C A075275 The parity of k is opposite to the parity of the differences.
%C A075275 a(23) > 3000. - _Michael S. Branicky_, Jan 20 2025
%e A075275 5 is a term because 5!! = 15 is the average of two successive primes, 13 and 17;
%e A075275 163 is a term because 163!! is the average of two successive primes, 163!! -+ 128.
%t A075275 PrevPrim[n_] := Block[{k = n - 1}, While[ !PrimeQ[k], k-- ]; k]; NextPrim[n_] := Block[{k = n + 1}, While[ !PrimeQ[k], k++ ]; k] Do[ a = n!!; If[ 2a == PrevPrim[a] + NextPrim[a], Print[n]], {n, 3, 762}]
%Y A075275 Cf. A053709. The differences between k!! and its neighboring primes are in A075453.
%K A075275 nonn,more
%O A075275 1,1
%A A075275 _Zak Seidov_, Sep 12 2002
%E A075275 Edited, corrected and extended by _Robert G. Wilson v_, Sep 16 2002
%E A075275 a(18)-a(22) from _Michael S. Branicky_, Jan 19 2025