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A077279 Last prime of n-th group of successive primes in A073684.

%I A077279 #9 May 23 2025 14:37:45
%S A077279 3,11,29,41,61,73,89,127,173,197,251,283,311,353,383,401,421,439,463,
%T A077279 487,503,523,569,599,983,1153,1511,1543,1601,1621,1721,1741,1783,1823,
%U A077279 1871,1901,2029,2239,2267,2281,2311,2341,2383,2447,2503,2539,2551,2591
%N A077279 Last prime of n-th group of successive primes in A073684.
%C A077279 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; A073683(n) is the first term in n-th group; A077279(n) is the last term in n-th group.
%o A077279 (Python)
%o A077279 from itertools import count, islice
%o A077279 from sympy import isprime, nextprime
%o A077279 def agen(): # generator of terms
%o A077279     s, i, p = 0, 1, 2
%o A077279     while True:
%o A077279         while not(isprime(s:=s+p)) or i < 2:
%o A077279             i, p = i+1, nextprime(p)
%o A077279         yield p
%o A077279         s, i, p = 0, 1, nextprime(p)
%o A077279 print(list(islice(agen(), 48))) # _Michael S. Branicky_, May 23 2025
%Y A077279 Cf. A073684, A092285, A073683.
%K A077279 nonn
%O A077279 1,1
%A A077279 _Zak Seidov_, Nov 02 2002