A273775 Smallest prime p > n + 1 where a base b exists with abs(b - p) = n such that b^(p-1) == 1 (mod p^2).

257, 23, 13, 229, 11, 13, 13, 599, 29, 109, 541, 29, 83, 4099, 2011, 23, 47, 2042851, 115981

Offset

4,1

Comments

Smallest p = prime(i) such that at least one of p-n or p+n occurs in the i-th row of A244249.

a(2) = 5. a(3) and a(23) are larger than 10^8 if they exist.

a(3) > 10^10, a(23) > 75*10^8. - Robert G. Wilson v, Dec 16 2016

Links

Table of n, a(n) for n=4..22.

Robert G. Wilson v, Table of n, a(n) for n = 2..1000, or 0 if no such value is known.

Example

For n = 4: p = 257 satisfies b^(p-1) == 1 (mod p^2) for b = p+4 = 261, i.e., 261^256 == 1 (mod 257^2) and is the smallest such p, so a(4) = 257.

Mathematica

f[n_] := Block[{p = NextPrime[n +1]}, While[ PowerMod[p - n, p -1, p^2] != 1 && PowerMod[p + n, p -1, p^2] != 1, q = p = NextPrime@ p]; p] (* Robert G. Wilson v, Dec 14 2016 *)

Prog

(PARI) a(n) = forprime(p=n+2, , my(b=p-n, c=p+n); if(Mod(b, p^2)^(p-1)==1 || Mod(c, p^2)^(p-1)==1, return(p)))

Crossrefs

Cf. A244249.

Sequence in context: A004217 A351309 A051333 * A182912 A276233 A252726

Adjacent sequences: A273772 A273773 A273774 * A273776 A273777 A273778

Keyword

nonn,hard,more

Author

Felix Fröhlich, Dec 11 2016

Status

approved