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 A258233 #12 Jun 08 2015 10:35:30 %S A258233 0,1,1,3,6,7,11,15,16,25,30,32,42,40,44,52,63,71,76,87,82,97,102,113, %T A258233 127,137,136,143,154,154,186,200,204,215,234,249,251,262,272,284,309, %U A258233 324,345,334,349,359,406,414,431,447,441,489,487,511,508 %N A258233 Number of ways to represent the n-th prime as arithmetic mean of three other primes. %C A258233 Differs from A071704: for n>1, if 3*prime(n)-4 is prime then a(n)=1+A071704(n), otherwise a(n)=A071704(n). %H A258233 Zak Seidov and Charles R Greathouse IV, <a href="/A258233/b258233.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 terms from Seidov) %e A258233 a(5)=6 as A000040(5)=11 and 11 has 6 representations as arithmetic mean of three other (not equal to 11) primes: %e A258233 11 = (2+2+29)/3=(3+7+23)/3 = (3+13+17)/3 = (5+5+23)/3 = (7+7+19)/3 = (7+13+13)/3. %o A258233 (PARI) a(n,p=prime(n))=my(s=0); forprime(q=p+2,3*p-4, my(t=3*p-q); forprime(r=max(t-q, 2),(3*p-q)\2, if(t!=p+r && isprime(t-r), s++))); s \\ _Charles R Greathouse IV_, Jun 04 2015 %Y A258233 Cf. A000040, A071703, A071704. %K A258233 nonn %O A258233 1,4 %A A258233 _Zak Seidov_, May 24 2015