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A349779 Pairs of integers i,j such that i+prime(i) and j+prime(j) are a pair of amicable numbers.

%I A349779 #26 Dec 03 2021 10:32:53
%S A349779 41,51,99525,104283,280899,295869,18378754,21937204,52084243,53107499,
%T A349779 163148785,166346021,179162279,183252051,212063283,244033955,
%U A349779 3731366783,4226663091,7134801326,7818930716,10469380661,12074408463,12445587194,12667334246,16055012737,17258948163
%N A349779 Pairs of integers i,j such that i+prime(i) and j+prime(j) are a pair of amicable numbers.
%H A349779 Juan Luis Varona, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL24/Varona/varona4.html">On the Solution of the Equation n = a*k + b*p_k by Means of an Iterative Method</a>, Journal of Integer Sequences, Vol. 24 (2021), Article 21.10.5.
%e A349779 41 + prime(41) = 41 + 179 = 220, 51 + prime(51) = 51 + 233 = 284, and (220, 284) is an amicable pair.
%o A349779 (Python)
%o A349779 from sympy import nextprime, divisor_sigma
%o A349779 d = dict()
%o A349779 j, p = 0, 0
%o A349779 while True:
%o A349779     j, p = j+1, nextprime(p)
%o A349779     n = j+p
%o A349779     a = divisor_sigma(n)-n
%o A349779     d[(n, a)] = j
%o A349779     if (a, n) in d:
%o A349779         print(d[(a, n)], j) # _Martin Ehrenstein_, Dec 02 2021
%Y A349779 Cf. A002025, A002046, A014688, A259180.
%K A349779 nonn
%O A349779 1,1
%A A349779 _Michel Marcus_, Nov 30 2021
%E A349779 a(7)-a(8) from _Amiram Eldar_, Nov 30 2021
%E A349779 a(9)-a(16) from _Michel Marcus_, Dec 01 2021
%E A349779 a(17)-a(26) from _Martin Ehrenstein_, Dec 03 2021