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

%I A385586 #27 Jul 08 2025 07:49:25
%S A385586 37,34687,65587,2089951,8161477,8340613,18927067,25855567,64346413,
%T A385586 95150203,238973101,257658061,277743397,322210813,349883707,578403913,
%U A385586 704710543,1121445337,1654635937,1741780693,1804380007,1963734061,2346701941,2360966173,2720420707,3232299517,4343250181,4925742973,8085909913,9044601133
%N A385586 Primes p such that there exists prime q < p such that sigma(p+1) = sigma(q+1) = p + q.
%C A385586 The primes p and q form a P(1, 1)-amicable pair. See Dimitrov link.
%H A385586 S. I. Dimitrov, <a href="https://arxiv.org/abs/2408.07387">Generalizations of amicable numbers</a>, arXiv:2408.07387 [math.NT], 2024.
%e A385586 (23, 37) is such a pair because sigma(23+1)=sigma(37+1) = 23 + 37.
%o A385586 (PARI) upto(n) = {
%o A385586     res = List();
%o A385586     forprime(p = 2, n,
%o A385586         s = sigma(p+1);
%o A385586         q = s - p;
%o A385586         if(q < p && isprime(q) && sigma(q+1) == s,
%o A385586             print([p, q]);
%o A385586             listput(res, p);
%o A385586         );
%o A385586     ); res
%o A385586 } \\ _David A. Corneth_, Jul 03 2025
%Y A385586 Cf. A000203, A000040, A063990, A008333, A259180, A385718.
%Y A385586 Subequence of A385705.
%K A385586 nonn
%O A385586 1,1
%A A385586 _S. I. Dimitrov_, Jul 03 2025
%E A385586 More terms from _David A. Corneth_, Jul 03 2025