A057230 Numbers k such that k = p+q = r+s with p*q = r*s = primorial number(A002110) (p*q) < (r*s).

31, 107, 391, 467, 34049, 67973, 176413

Offset: 1

Author

Naohiro Nomoto, Sep 19 2000

Keywords

• nonn
• more

Comments

The corresponding pairs of primorials are (3#, 4#), (4#, 5#), (5#, 6#), (5#, 6#), (7#, 9#), (8#, 9#), (8#, 10#). No other terms found up to 23#. - Michel Marcus, Feb 21 2016

a(8) > 3203982595205562774973. - Sean A. Irvine, May 26 2022

Examples

			31 = 30+1 = 21+10, where 30=30*1 and 210=21*10 are primorial numbers.
		

Links

• Sean A. Irvine, Java program (github)

Crossrefs

Cf. A002110, A006862, A182987.

Programs

PARI

isprimo(n) = {if (n==1, return (1)); if (!issquarefree(n), return(0)); f = factor(n); #f~ == primepi(vecmax(f[,1]));}
isok(n) = {c = 0; for (na=1, n\2, if (isprimo(na*(n - na)), c++); if (c == 2, return(1)););} \\ Michel Marcus, Feb 20 2016