A245177 - OEIS

%I #28 Jul 28 2020 08:50:07

%S 5,13,19,23,29,31,43,53,59,61,67,73,79,83,89,97,103,131,137,151,157,

%T 163,173,179,181,191,197,199,211,229,233,239,241,281,293,307,317,347,

%U 359,367,373,379,389,397,409,419,421,431,433,443,449

%N Inefficient primes.

%C A prime p is inefficient (see Amdeberhan - Moll) if it divides A000085(n) for some n < p.

%H Robert Israel, <a href="/A245177/b245177.txt">Table of n, a(n) for n = 1..1428</a>

%H 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 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 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 N:= 1000:  # to get all terms <= N

%p I1:= proc(n) option remember;  I1(n-1)+(n-1)*I1(n-2) end proc:

%p I1(0):= 1: I1(1):= 1:

%p Primes:= select(isprime,{2,seq(2*i+1,i=1..floor((N-1)/2))}):

%p PP:= convert(Primes,`*`):

%p A:= {}:

%p for n from 1 to N-1 do

%p   g:= igcd(I1(n),PP):

%p   A:= A union select(`>`,numtheory:-factorset(g),n);

%p od:

%p A; # _Robert Israel_, Jul 20 2014

%t A85 = DifferenceRoot[Function[{y, n}, {(-n-1) y[n] - y[n+1] + y[n+2] == 0, y[1] == 1, y[2] == 2}]];

%t inefficientQ[p_] := AnyTrue[Range[p-1], Divisible[A85[#], p]&];

%t 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 Cf. A000085. See A264737 for another version.

%K nonn

%O 1,1

%A _N. J. A. Sloane_, Jul 19 2014