A242754 Positive integers k such that k*p == 1 (mod prime(k)) for some prime p < prime(k).

2, 3, 4, 6, 7, 10, 11, 13, 17, 18, 21, 31, 37, 40, 41, 46, 48, 49, 52, 53, 58, 60, 64, 66, 70, 71, 72, 73, 75, 81, 85, 92, 93, 96, 100, 102, 109, 117, 119, 127, 136, 137, 140, 143, 145, 146, 149, 160, 162, 179, 189, 194, 200, 206, 215, 232, 233, 243, 246, 247

Offset: 1

Author

Zhi-Wei Sun, May 22 2014

Keywords

• nonn

Comments

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

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

Examples

			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.
		

Links

• Zhi-Wei Sun, Table of n, a(n) for n = 1..10000

Crossrefs

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

Programs

Mathematica

p[n_]:=PrimeQ[PowerMod[n,-1,Prime[n]]]
n=0;Do[If[p[k],n=n+1;Print[n," ",k]];Continue,{k,1,247}]