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%I #10 Jun 09 2017 09:23:18
%S 3,43,8237,14533,26153,11314271
%N Odd primes p such that p^2 divides A001205(p)-(p-1)/2.
%C 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.
%C a(7) > 2.3*10^7. - _Giovanni Resta_, Jun 04 2017
%H Leonard Carlitz, <a href="http://www.jstor.org/stable/2307904">Congruences for the Number of n-Gons Formed by n Lines</a>, The American Mathematical Monthly, Vol. 61, No. 6 (1954), pp. 407-411.
%t 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
%Y Cf. A001205.
%K nonn,more
%O 1,1
%A _Amiram Eldar_, Jun 03 2017
%E a(6) from _Giovanni Resta_, Jun 04 2017
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