This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A073683 #10 May 23 2025 15:31:23
%S A073683 2,5,13,31,43,67,79,97,131,179,199,257,293,313,359,389,409,431,443,
%T A073683 467,491,509,541,571,601,991,1163,1523,1549,1607,1627,1723,1747,1787,
%U A073683 1831,1873,1907,2039,2243,2269,2287,2333,2347,2389,2459,2521,2543,2557,2593
%N A073683 Group the primes such that the sum of each group is a prime. Each group from the second onwards should contain at least 3 primes: (2, 3), (5, 7, 11), (13, 17, 19, 23, 29), (31, 37, 41), (43, 47, 53, 59, 61), ... This is the sequence of the leading element in each group.
%C A073683 First prime of n-th group of successive primes in A073684.
%e A073683 Partition the sequence of primes into groups so that the sum of the terms in each group is prime: {2, 3}, {5, 7, 11}, {13, 17, 19, 23, 29}, {31, 37, 41}, {43, 47, 53, 59, 61}, {67, 71, 73}, {79, 83, 89}, {97, 101, 103, 107, 109, 113, 127}, {131, 137, 139, 149, 151, 157, 163, 167, 173}, {179, 181, 191, 193, 197},..; A073684(n) is the number of terms in n-th group; A073682(n) is the sum of terms in n-th group; a(n) is the first term in n-th group; A077279(n) is the last term in n-th group.
%o A073683 (Python)
%o A073683 from itertools import count, islice
%o A073683 from sympy import isprime, nextprime
%o A073683 def agen(): # generator of terms
%o A073683 s, i, p = 0, 1, 2
%o A073683 while True:
%o A073683 pp = p
%o A073683 while not(isprime(s:=s+p)) or i < 2:
%o A073683 i, p = i+1, nextprime(p)
%o A073683 yield pp
%o A073683 s, i, p = 0, 1, nextprime(p)
%o A073683 print(list(islice(agen(), 49))) # _Michael S. Branicky_, May 23 2025
%Y A073683 Cf. A073682, A073684, A077279.
%K A073683 nonn
%O A073683 1,1
%A A073683 _Amarnath Murthy_, Aug 11 2002
%E A073683 More terms from _Zak Seidov_, Nov 02 2002