A376032 - OEIS

A376032

Least prime p that does not divide n such that 2^phi(n) == 1 (mod p), or 0 if no such prime exists.

0, 0, 0, 3, 3, 0, 3, 3, 7, 3, 3, 5, 3, 3, 17, 3, 3, 7, 3, 3, 5, 3, 3, 5, 3, 3, 7, 3, 3, 17, 3, 3, 5, 3, 3, 5, 3, 3, 5, 3, 3, 5, 3, 3, 7, 3, 3, 5, 3, 3, 5, 3, 3, 7, 3, 3, 5, 3, 3, 17, 3, 3, 5, 3, 3, 5, 3, 3, 5, 3, 3, 5, 3, 3, 11, 3, 3, 5, 3, 3, 7, 3, 3, 5, 3, 3

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OFFSET

1,4

COMMENTS

There is such a prime for all n except for n = 1, 2, 3, and 6.

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000

C. A. Nicol and J. L. Selfridge, Problem E 3452, Elementary Problems, The American Mathematical Monthly, Vol. 98, No. 7 (1991), p. 645; Extraneous Primes, Solution to Problem E 3452 by David Callan and Kenneth Rogers, ibid., Vol. 100, No. 4 (1993), p. 404; Comment by Gerry Myerson, ibid., Vol. 100, No. 10 (1993), p. 959.

MATHEMATICA

a[n_] := Module[{phi = EulerPhi[n], p = 2}, While[Divisible[n, p] || PowerMod[2, phi, p] != 1, p = NextPrime[p]]; p]; a[1] = a[2] = a[3] = a[6] = 0; Array[a, 100]

PROG

(PARI) a(n) = {my(phi = eulerphi(n), p = 2); if(6 % n == 0, 0, while(!(n%p) || Mod(2, p)^phi != 1, p = nextprime(p+1)); p); }

CROSSREFS

Cf. A000010 (phi).

Sequence in context: A036477 A330013 A128164 * A339702 A260636 A245256

Adjacent sequences: A376029 A376030 A376031 * A376033 A376034 A376035

KEYWORD

nonn,easy

AUTHOR

Amiram Eldar, Sep 07 2024

STATUS

approved