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Positive integers k such that k*p == 1 (mod prime(k)) for some prime p < prime(k).
5

%I #14 May 23 2014 00:43:41

%S 2,3,4,6,7,10,11,13,17,18,21,31,37,40,41,46,48,49,52,53,58,60,64,66,

%T 70,71,72,73,75,81,85,92,93,96,100,102,109,117,119,127,136,137,140,

%U 143,145,146,149,160,162,179,189,194,200,206,215,232,233,243,246,247

%N Positive integers k such that k*p == 1 (mod prime(k)) for some prime p < prime(k).

%C According to the conjecture in A242753, this sequence should have infinitely many terms.

%C Conjecture: The number of terms not exceeding x > 1 has the main term x/(log x) as x tends to infinity.

%H Zhi-Wei Sun, <a href="/A242754/b242754.txt">Table of n, a(n) for n = 1..10000</a>

%e a(4) = 6 since 6*11 == 1 (mod prime(6)=13) with 11 prime, but 5*9 == 1 (mod prime(5)=11) with 9 composite.

%t p[n_]:=PrimeQ[PowerMod[n,-1,Prime[n]]]

%t n=0;Do[If[p[k],n=n+1;Print[n," ",k]];Continue,{k,1,247}]

%Y Cf. A000040, A000720, A242425, A242748, A242750, A242752, A242753, A242755.

%K nonn

%O 1,1

%A _Zhi-Wei Sun_, May 22 2014