A173912 - OEIS

%I #21 Sep 28 2020 05:33:00

%S 3,5,7,13,17,19,23,31,33,51,61,71,89,101,107,127,139,191,271,273,305,

%T 331,347,351,367,397,405,407,427,435,457,467,489,521,525,539,543,549,

%U 559,565,577,583,589,597,601,607,611,613,617,619,641,643,661,693,717,729,787,793,809,817,819,837,871,879,891,899,983,987,991

%N Numbers x that when put through Lucas-Lehmer tests give a residue that has a digital root of 0 or 9.

%C The PARI code uses a function that assumes 0 has a digital root of 9.

%C Note: since I allowed 0 to count as having digital root 9, all Mersenne prime exponents > 2 will be a subsequence of this sequence.

%t lucaslehmer2Q[p_] := Module[{s = 4, x}, For[x = 1, x <= p-2, x++, s = Mod[s^2 - 2, 2^p - 1]; If[x == p-2 && sumdigits1[s] == 9, Return[True]]]; False];

%t sumdigits1[n_] := If[Mod[n, 9] != 0, Mod[n, 9], 9];

%t Select[Range[1000], lucaslehmer2Q] (* _Jean-François Alcover_, Sep 28 2020, after PARI *)

%o (PARI) lucaslehmer2(p) = s=4; for(x=1, p-2, s=(s^2-2)%(2^p-1)); if(x=p-2 && sumdigits1(s)==9, print1(p", "))

%o sumdigits1(n)=if(n%9!=0,n%9,9)

%o for(x=1,1000,lucaslehmer2(x))

%K nonn,base

%O 1,1

%A _Roderick MacPhee_, Nov 26 2010