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Values of n such that 4j = np+1 where p = 8x+1, x integer, p prime and j mod 3 = 0.

a(n) is the least k such that k * A007519(n) + 1 = 0 (mod 12).

7, 7, 11, 7, 11, 7, 7, 11, 7, 11, 7, 7, 11, 11, 7, 7, 11, 11, 7, 11, 7, 7, 11, 7, 11, 7, 7, 11, 7, 11, 7, 11, 7, 7, 7, 11, 7, 7, 11, 11, 7, 7, 11, 11, 7, 11, 7, 11, 7, 11, 11, 7, 7, 7, 7, 11, 7, 7, 11, 11, 7, 7, 11, 11, 11, 7, 7, 11, 7, 7, 11, 11, 7, 11, 11, 7, 7, 11, 7

0,1,1

Original name: Values of n such that 4j = np+1 where p = 8x+1, x integer, p prime and j mod 3 = 0.

E.g. x=2 gives pFor example, A007519(1)=17. , 4j=17p+1 implies n k is 7 and j is 30. The values that give 7 form the basis for solutions for the Erdős-Straus conjecture: 4/n=1/a+1/b+1/c for n >= 2, a,b,c>0 and integers.

Entry revised by Sean A. Irvine, Jul 14 2023

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E.g. x=2 gives p=17. 4j=17p+1 implies n is 7 and j is 30. The values that give 7 form the basis for solutions for the ErdosErdős-Strauss Straus conjecture: 4/n=1/a+1/b+1/c for n >= 2, a,b,c>0 and integers.

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_Jon Perry (perry(AT)globalnet.co.uk), _, Oct 05 2001

Values of n such that 4j = np+1 where p = 8x+1, x integer, p prime and j mod 3 = 0.

7, 7, 11, 7, 11, 7, 7, 11, 7, 11, 7, 7, 11, 11, 7, 7, 11, 11, 7, 11, 7, 7, 11, 7, 11, 7, 7, 11, 7, 11, 7, 11, 7, 7, 7, 11, 7, 7, 11, 11, 7, 7, 11, 11, 7, 11, 7, 11, 7, 11, 11, 7, 7, 7, 7, 11, 11, 7, 7, 11, 11, 11, 7, 7, 11, 7, 11, 11, 11, 11, 7, 7, 11

0,1

H. Mishima, <a href="http://www.asahi-net.or.jp/~KC2H-MSM/mathland/overview.htm">Overview of "Mathematician's Secret Room"</a>

E.g. x=2 gives p=17. 4j=17p+1 implies n is 7 and j is 30. The values that give 7 form the basis for solutions for the Erdos-Strauss conjecture: 4/n=1/a+1/b+1/c for n >= 2, a,b,c>0 and integers.

nonn

Jon Perry (perry(AT)globalnet.co.uk), Oct 05 2001

approved