A210186
a(n) = least integer m>1 such that m divides none of P_i + P_j with 0
2, 3, 5, 7, 11, 19, 23, 23, 23, 47, 59, 61, 71, 71, 71, 101, 101, 101, 101, 101, 101, 113, 113, 113, 113, 113, 113, 113, 113, 113, 223, 223, 223, 223, 223, 223, 223, 223, 223, 223, 223, 223, 223, 223, 223, 223, 223, 223, 487, 487, 661, 661, 661, 661, 661, 661, 661, 661, 661, 719, 719, 719, 719, 719, 719, 811, 811, 811, 811, 811, 811, 811, 811, 811, 811
Offset: 1
Keywords
Examples
We have a(3)=5 since 2+2*3, 2+2*3*5, 2*3+2*3*5 are pairwise distinct modulo m=5 but not pairwise distinct modulo m=2,3,4.
Links
- Zhi-Wei Sun, Table of n, a(n) for n = 1..258
- Romeo Meštrović, Euclid's theorem on the infinitude of primes: a historical survey of its proofs (300 BC--2012) and another new proof, arXiv preprint arXiv:1202.3670 [math.HO], 2012-2018. - From _N. J. A. Sloane_, Jun 13 2012
- Zhi-Wei Sun, A function taking only prime values, message to Number Theory List, Feb. 21, 2012.
- Zhi-Wei Sun, On functions taking only prime values, J. Number Theory, Vol. 133, No. 8 (2013), pp. 2794-2812.
Programs
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Mathematica
P[n_]:=Product[Prime[k],{k,1,n}] R[n_,m_]:=Product[If[Mod[P[k]+P[j],m]==0,0,1],{k,2,n},{j,1,k-1}] Do[Do[If[R[n,m]==1,Print[n," ",m];Goto[aa]],{m,2,Max[2,n^2]}]; Print[n];Label[aa];Continue,{n,1,300}]
Comments