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 A211376 #31 Jul 18 2021 11:25:17
%S A211376 2,4,6,6,6,12,6,12,12,6,12,24,6,6,12,18,6,12,6,18,24,18,30,12,6,6,30,
%T A211376 24,24,18,30,12,18,12,6,36,30,6,12,18,60,30,30,72,12,60,30,48,6,12,30,
%U A211376 12,6,6,12,60,6,12,54,24,24,48,36,36,18,30,36,18,6,90
%N A211376 a(n) is the smallest 5-smooth number k such that both prime(n) - k and prime(n) + k are prime.
%C A211376 The three numbers prime(n) - k, prime(n), prime(n) + k are an arithmetic progression of primes.
%C A211376 Conjecture: a(n) is defined for all integers n > 2.
%C A211376 Conjecture confirmed true up to n = 300000, no exceptions.
%C A211376 Note that if (p1, n, p2) is an arithmetic progression where p1 and p2 are prime, then 2n = p1 + p2 is a Goldbach pair. There are numbers n such that no such sequence (p1, n, p2) exists for which the common difference n - p1 = p2 - n is 5-smooth. The first such number is 90. The first such odd number is 1845.
%C A211376 a(n) is defined for 3 <= n <= 10^7. - _David A. Corneth_, Jul 10 2021
%H A211376 Lei Zhou, <a href="/A211376/b211376.txt">Table of n, a(n) for n = 3..10000</a>
%e A211376 Let n = 43. The 43rd prime is 191, and 191-42 = 149 and 191+42 = 233 are both prime. However, 42 = 2*3*7 is not a 5-smooth number, so a(43) != 42. But 191-60 = 31 and 191+60 = 251 are both prime numbers, and 60 = 2^2*3*5 is the smallest such 5-smooth number. So a(43) = 60.
%t A211376 Table[p=Prime[i];j=0;While[j=j+2;If[(PrimeQ[p-j])&&(PrimeQ[p+j]), f=Last[FactorInteger[j]][[1]],f=p];f>5];j,{i,3,72}]
%Y A211376 Cf. A078611, A051037, A001031.
%K A211376 nonn,easy
%O A211376 3,1
%A A211376 _Lei Zhou_, Feb 07 2013