A308270 - OEIS

A308270

Smallest prime with E-irregularity index n.

2, 5, 307, 277

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,1

COMMENTS

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.

LINKS

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

PROG

(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

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))))

CROSSREFS

KEYWORD

nonn,hard,more

AUTHOR

STATUS

approved