A222114 Least integer m>1 such that 6*p_k*(p_k-1) (k=1,...,n) are pairwise incongruent modulo m, where p_k denotes the k-th prime.

2, 5, 5, 13, 19, 29, 31, 37, 37, 37, 61, 61, 61, 89, 97, 97, 97, 109, 131, 139, 149, 157, 157, 157, 173, 181, 193, 193, 193, 193, 241, 241, 241, 271, 271, 271, 271, 317, 331, 331, 331, 349, 349, 367, 367, 367, 397, 397, 397, 397, 397, 397, 457, 457, 457, 457, 457, 457, 523, 523

Offset: 1

Author

Zhi-Wei Sun, May 13 2013

Keywords

• nonn

Comments

Conjecture: For each n=3,4,..., a(n) is the first prime p>=p_n dividing none of those p_i+p_j-1 (1<=i

Examples

			a(2)=5 since 6*p_1*(p_1-1)=12 and 6*p_2*(p_2-1)=36 are incongruent modulo 5 but 12 is congruent to 36 modulo any of 2, 3, 4.
		

Links

• Zhi-Wei Sun, Table of n, a(n) for n = 1..10000
• Zhi-Wei Sun, On functions taking only prime values, J. Number Theory, 133 (2013), 2794-2812.

Crossrefs

Cf. A000040, A208643, A181901.

Programs

Mathematica

R[n_,m_]:=Union[Table[Mod[6Prime[k](Prime[k]-1),m],{k,1,n}]]
s=2
Do[Do[If[Length[R[n,m]]==n,s=m;Print[n," ",m];Goto[aa]],{m,s,n^2}];
Print[n];Label[aa];Continue,{n,1,100}]

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