A316348 a(n) is the smallest k > 1 such that gcd(k, m^k - m) = 1 for all m = 2,...,n.

35, 35, 77, 77, 143, 143, 143, 143, 299, 299, 323, 323, 323, 323, 437, 437, 667, 667, 667, 667, 899, 899, 899, 899, 899, 899, 1457, 1457, 1739, 1739, 1739, 1739, 1739, 1739, 1763, 1763, 1763, 1763, 2021, 2021, 2491, 2491, 2491, 2491, 3127, 3127, 3127, 3127, 3127

Offset

2,1

Comments

Conjecture: all the terms are in A121707.

From David A. Corneth, Aug 13 2018: (Start)

GCD(n, a(n)) = 1. a(n) is odd.

Is a(n) squarefree?

a(n+1) >= a(n) by definition. (End)

It seems that a(prime(n+1)-1) > a(prime(n)-1) for n > 1. - Thomas Ordowski, Aug 13 2018

Links

Michel Marcus, Table of n, a(n) for n = 2..306

Formula

Conjecture: a(n) ~ n^2.

Prog

(PARI) isok(k, n)= {for (m=2, n, if (gcd(k, m^k - m) != 1, return (0)); ); return(1); }
a(n) = {my(k=2); while (! isok(k, n), k++); k; } \\ Michel Marcus, Aug 13 2018

Crossrefs

Cf. A121707, A267999, A316111.

Sequence in context: A257948 A142728 A316111 * A146205 A201067 A210320

Adjacent sequences: A316345 A316346 A316347 * A316349 A316350 A316351

Keyword

nonn

Author

Thomas Ordowski, Aug 13 2018

Extensions

More terms from Michel Marcus, Aug 13 2018

Status

approved