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A173702 Partial sums of prime numbers of measurement A002049.

%I A173702 #13 Sep 02 2025 14:11:10
%S A173702 1,4,11,23,43,73,117,176,251,347,465,608,777,974,1204,1468,1767,2102,
%T A173702 2475,2888,3343,3844,4393,4991,5639,6340,7098,7916,8796,9740,10749,
%U A173702 11828,12984,14220,15537,16937
%N A173702 Partial sums of prime numbers of measurement A002049.
%C A173702 Prime partial sums of prime numbers of measurement begin: 11, 23, 43, 73, 251, 347, 3343, 5639, 16937. The subsequence of squares begins: 1, 4, 3844 = 2^2 * 31^2.
%H A173702 Chai Wah Wu, <a href="/A173702/b173702.txt">Table of n, a(n) for n = 1..10000</a>
%F A173702 a(n) = Sum_{i=1..n} A002049(i).
%e A173702 a(10) =  1 + 3 + 7 + 12 + 20 + 30 + 44 + 59 + 75 + 96 = 347 is prime.
%o A173702 (Python)
%o A173702 from itertools import count, accumulate, islice
%o A173702 from collections import deque
%o A173702 def A173702_gen(): # generator of terms
%o A173702     aset, alist, a, b = set(), deque(), 0, 0
%o A173702     for k in count(1):
%o A173702         if k in aset:
%o A173702             aset.remove(k)
%o A173702         else:
%o A173702             a += k
%o A173702             yield (b:=a+b)
%o A173702             aset |= set(k+d for d in accumulate(alist))
%o A173702             alist.appendleft(k)
%o A173702 A173702_list = list(islice(A173702_gen(),50)) # _Chai Wah Wu_, Sep 02 2025
%Y A173702 Cf. A002049.
%K A173702 nonn,changed
%O A173702 1,2
%A A173702 _Jonathan Vos Post_, Nov 25 2010