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 A308243 #7 May 26 2019 14:59:54 %S A308243 0,0,1,0,0,1,1,1,0,1,1,1,1,1,1,1,0,1,1,1,1,1,0,1,1,1,0,0,1,1,0,0,1,1, %T A308243 1,0,1,0,0,1,0,1,0,1,1,0,0,1,0,1,1,0,1,1,1,1,1,0,3,1,0,1,2,2,1,1,0,1, %U A308243 0,3,1,1,0,1,1,0,1,1,1,1,1,1,0,1,0,0,1 %N A308243 Index of E-irregularity of prime(n). %C A308243 A prime p >= 5 is an E-irregular prime if there is an even integer 2*k such that 2 <= 2*k <= p-3 and p divides E(2*k), where E(i) is the i-th Euler number (A000364). The pair (p, 2*k) is called an E-irregular pair. The number of such pairs for a given p is called the index of E-irregularity of p (cf. Ernvall, Metsänkylä, 1978, p. 618). %C A308243 In other words, a prime p is E-irregular if its index of E-irregularity is > 0, which is the case if p is a term of A092218. Otherwise, p is E-regular and is a term of A092217. %H A308243 R. Ernvall and T. Metsänkylä, <a href="https://doi.org/10.1090/S0025-5718-1978-0482273-9">Cyclotomic invariants and E-irregular primes</a>, Mathematics of Computation 32 (1978), 617-629. %o A308243 (PARI) a000364(n) = subst(bernpol(2*n+1), 'x, 1/4)*4^(2*n+1)*(-1)^(n+1)/(2*n+1) \\ after _Charles R Greathouse IV_ in A000364 %o A308243 a(n) = my(p=prime(n), e=2, i=0); while(e <= p-3, if(a000364(e)%p==0, i++); e=e+2); i %Y A308243 Cf. A000364, A092217, A092218, A120337. %K A308243 nonn %O A308243 1,59 %A A308243 _Felix Fröhlich_, May 16 2019