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A245177 Inefficient primes.

%I A245177 #28 Jul 28 2020 08:50:07
%S A245177 5,13,19,23,29,31,43,53,59,61,67,73,79,83,89,97,103,131,137,151,157,
%T A245177 163,173,179,181,191,197,199,211,229,233,239,241,281,293,307,317,347,
%U A245177 359,367,373,379,389,397,409,419,421,431,433,443,449
%N A245177 Inefficient primes.
%C A245177 A prime p is inefficient (see Amdeberhan - Moll) if it divides A000085(n) for some n < p.
%H A245177 Robert Israel, <a href="/A245177/b245177.txt">Table of n, a(n) for n = 1..1428</a>
%H A245177 Tewodros Amdeberhan and Victor H. Moll, <a href="http://dauns.math.tulane.edu/~vhm/papers_html/invo-may12.pdf">Involutions and their progenies</a>, preprint, 2014.
%H A245177 Tewodros Amdeberhan and Victor H. Moll, <a href="https://arxiv.org/abs/1406.2356">Involutions and their progenies</a>, arXiv:1406.2356 [math.CO], 2014.
%H A245177 Tewodros Amdeberhan and Victor H. Moll, <a href="https://dx.doi.org/10.4310/JOC.2015.v6.n4.a5">Involutions and their progenies</a>, Journal of Combinatorics, 6(4) (2015), 483-508.
%p A245177 N:= 1000:  # to get all terms <= N
%p A245177 I1:= proc(n) option remember;  I1(n-1)+(n-1)*I1(n-2) end proc:
%p A245177 I1(0):= 1: I1(1):= 1:
%p A245177 Primes:= select(isprime,{2,seq(2*i+1,i=1..floor((N-1)/2))}):
%p A245177 PP:= convert(Primes,`*`):
%p A245177 A:= {}:
%p A245177 for n from 1 to N-1 do
%p A245177   g:= igcd(I1(n),PP):
%p A245177   A:= A union select(`>`,numtheory:-factorset(g),n);
%p A245177 od:
%p A245177 A; # _Robert Israel_, Jul 20 2014
%t A245177 A85 = DifferenceRoot[Function[{y, n}, {(-n-1) y[n] - y[n+1] + y[n+2] == 0, y[1] == 1, y[2] == 2}]];
%t A245177 inefficientQ[p_] := AnyTrue[Range[p-1], Divisible[A85[#], p]&];
%t A245177 Reap[For[p = 2, p < 1000, p = NextPrime[p], If[inefficientQ[p], Print[p]; Sow[p]]]][[2, 1]] (* _Jean-François Alcover_, Jul 28 2020 *)
%Y A245177 Cf. A000085. See A264737 for another version.
%K A245177 nonn
%O A245177 1,1
%A A245177 _N. J. A. Sloane_, Jul 19 2014