A385739 Primes p such that there exists a prime q < p such that sigma(q-1) = sigma(p+1) = p + q.

5563, 203431, 389923, 901423, 5495263, 7418863, 28128367, 188953969, 210627577, 392753209, 402877087, 505757683, 619418689, 2549153611, 2580356851, 3953660383, 5692944349, 6806206831, 6894059071, 7082199673, 10058113363, 11307503629, 12601725943, 12615171649

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. Apparently (q-1, p+1) is an amicable pair A259180.

Examples

			(5021, 5563) is such a pair because sigma(5021-1) = sigma(5563+1) = 5021 + 5563.
		

Links

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

Crossrefs

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

Extensions

a(5)-a(13) from Michel Marcus, Jul 08 2025

a(14)-a(24) from Giorgos Kalogeropoulos, Jul 14 2025