A385586 Primes p such that there exists prime q < p such that sigma(p+1) = sigma(q+1) = p + q.

37, 34687, 65587, 2089951, 8161477, 8340613, 18927067, 25855567, 64346413, 95150203, 238973101, 257658061, 277743397, 322210813, 349883707, 578403913, 704710543, 1121445337, 1654635937, 1741780693, 1804380007, 1963734061, 2346701941, 2360966173, 2720420707, 3232299517, 4343250181, 4925742973, 8085909913, 9044601133

Offset: 1

Author

S. I. Dimitrov, Jul 03 2025

Keywords

• nonn

Comments

The primes p and q form a P(1, 1)-amicable pair. See Dimitrov link.

Examples

			(23, 37) is such a pair because sigma(23+1)=sigma(37+1) = 23 + 37.
		

Links

• S. I. Dimitrov, Generalizations of amicable numbers, arXiv:2408.07387 [math.NT], 2024.

Crossrefs

Cf. A000203, A000040, A063990, A008333, A259180, A385718.

Subequence of A385705.

Programs

PARI

upto(n) = {
    res = List();
    forprime(p = 2, n,
        s = sigma(p+1);
        q = s - p;
        if(q < p && isprime(q) && sigma(q+1) == s,
            print([p, q]);
            listput(res, p);
        );
    ); res
} \\ David A. Corneth, Jul 03 2025

Extensions

More terms from David A. Corneth, Jul 03 2025