A308243 -id:A308243 - cp's OEIS frontend

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A308270 Smallest prime with E-irregularity index n.

Original entry on oeis.org

2, 5, 307, 277

Offset: 0

Felix Fröhlich, May 17 2019

Smallest prime p such that A308243(i) = n, where i is the index of p in A000040.
E-regular primes have E-irregularity index 0, so a(0) = 2, since 2 is the smallest E-regular prime (A092217).
Does such a prime exist for every n?
a(4) > 2003 if it exists.

R. Ernvall and T. Metsänkylä, Cyclotomic invariants and E-irregular primes, Mathematics of Computation 32 (1978), 617-629.

Cf. A000040, A061576, A092217, A308243.

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
a308243(n) = my(p=prime(n), e=2, i=0); while(e <= p-3, if(a000364(e)%p==0, i++); e=e+2); i
a(n) = for(x=1, oo, if(a308243(x)==n, return(prime(x))))

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