A057230 - OEIS

%I #22 May 26 2022 20:43:26

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

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

%C 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

%C a(8) > 3203982595205562774973. - _Sean A. Irvine_, May 26 2022

%H Sean A. Irvine, <a href="https://github.com/archmageirvine/joeis/blob/master/src/irvine/oeis/a057/A057230.java">Java program</a> (github)

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

%o (PARI) isprimo(n) = {if (n==1, return (1)); if (!issquarefree(n), return(0)); f = factor(n); #f~ == primepi(vecmax(f[,1]));}

%o 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

%Y Cf. A002110, A006862, A182987.

%K nonn,more

%O 1,1

%A _Naohiro Nomoto_, Sep 19 2000