A385740 Primes p such that there exists a prime q < p such that sigma(p-1) = sigma(q-1) = p + q.

1163, 7583, 17099, 48857, 65963, 172859, 5408423, 6804047, 19247087, 73162367, 77695043, 109775657, 109871933, 116464757, 160454717, 175031957, 175288493, 218543393, 268382183, 303220769, 379299989, 705800723, 823155779, 889218389, 967371143, 1100618483, 1242282407, 1701133163

Offset: 1

Author

S. I. Dimitrov, Jul 08 2025

Keywords

• nonn
• hard

Comments

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

Examples

			(853, 1163) is such a pair because sigma(853-1) = sigma(1163-1) = 853 + 1163.
		

Links

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

Crossrefs

Cf. A000040, A000203, A063990, A008333, A259180, A385586, A385718, A385739.

Extensions

a(6)-a(25) from Michel Marcus, Jul 08 2025

a(26)-a(28) from Giorgos Kalogeropoulos, Jul 14 2025