A287959 Odd primes p such that p^2 divides A001205(p)-(p-1)/2.

3, 43, 8237, 14533, 26153, 11314271

Offset: 1

Author

Amiram Eldar, Jun 03 2017

Keywords

• nonn
• more

Comments

Carlitz proved that A001205(p) == (p-1)/2 (mod p) for all odd primes p. This sequence consists of odd primes for which A001205(p) == (p-1)/2 (mod p^2) holds.

a(7) > 2.3*10^7. - Giovanni Resta, Jun 04 2017

Links

• Leonard Carlitz, Congruences for the Number of n-Gons Formed by n Lines, The American Mathematical Monthly, Vol. 61, No. 6 (1954), pp. 407-411.

Crossrefs

Cf. A001205.

Programs

Mathematica

a[1] = 0; a[2] = 0; a[3] = 1; a[n_] := a[n] = (n - 1)*(a[n - 1] + (n - 2)*a[n - 3]/2); lst = {}; k = 3; While[Length[lst] < 5, If[PrimeQ[k] && Divisible[a[k] - (k - 1)/2, k^2], lst = AppendTo[lst, k]]; k++]; lst

Extensions

a(6) from Giovanni Resta, Jun 04 2017