This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
1*(2^2-1)*(1*(2^2-1)+1)+1=13 prime, 2^2-1 first Mersenne prime, a(1)=1 2*(2^3-1)*(2*(2^3-1)+1)+1=211 prime, 2^3-1 second Mersenne prime, a(2)=2
M(4)=2^7-1=127 127^2+127-1=16255 composite (2*127)^2+2*127-1=64769 composite (3*127)^2+3*127-1=145541 composite (4*127)^2+4*127-1=258571 composite (5*127)^2+5*127-1=403859 composite (6*127)^2+6*127-1=581405 composite (7*127)^2+7*127-1=791209 prime so k(4)=7 1*(2^2-1)*(1*(2^2-1)+1)-1=11 prime, 2^2-1 first Mersenne prime, a(1)=1. 3*(2^3-1)*(3*(2^3-1)+1)-1=461 prime, 2^3-1 second Mersenne prime, a(2)=3. n=6: Mp(6) = 131071 and 19*131071*(19*131071 + 1) - 1 = 6201840632149 which is prime, and for k=1..18 no prime appears. - _Wolfdieter Lang_, Oct 26 2014
lista() = {v = readvec("b000043.txt"); for (i=1, #v, mp = 2^v[i] - 1; k=1; while (!isprime(k*mp*(k*mp + 1) - 1), k++); print1(k, ", "););} \\ Michel Marcus, Oct 27 2014
1*(2^2-1)*(1*(2^2-1)-1)-1=5 prime, 2^2-1 first Mersenne prime, a(1)=1; 1*(2^3-1)*(1*(2^3-1)-1)-1=41 prime, 2^3-1 second Mersenne prime, a(2)=1.
1*(2^2-1)*(1*(2^2-1)-1)+1=7 prime, 2^2-1 first Mersenne prime, a(1)=1; 1*(2^3-1)*(1*(2^3-1)-1)+1=43 prime, 2^3-1 second Mersenne prime, a(2)=1.
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