A173702 Partial sums of prime numbers of measurement A002049.

1, 4, 11, 23, 43, 73, 117, 176, 251, 347, 465, 608, 777, 974, 1204, 1468, 1767, 2102, 2475, 2888, 3343, 3844, 4393, 4991, 5639, 6340, 7098, 7916, 8796, 9740, 10749, 11828, 12984, 14220, 15537, 16937

Offset

1,2

Comments

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.

Links

Chai Wah Wu, Table of n, a(n) for n = 1..10000

Formula

a(n) = Sum_{i=1..n} A002049(i).

Example

a(10) =  1 + 3 + 7 + 12 + 20 + 30 + 44 + 59 + 75 + 96 = 347 is prime.

Prog

(Python)
from itertools import count, accumulate, islice
from collections import deque
def A173702_gen(): # generator of terms
    aset, alist, a, b = set(), deque(), 0, 0
    for k in count(1):
        if k in aset:
            aset.remove(k)
        else:
            a += k
            yield (b:=a+b)
            aset |= set(k+d for d in accumulate(alist))
            alist.appendleft(k)
A173702_list = list(islice(A173702_gen(), 50)) # Chai Wah Wu, Sep 02 2025

Crossrefs

Cf. A002049.

Sequence in context: A301165 A019298 A237586 * A244281 A014242 A240074

Adjacent sequences: A173699 A173700 A173701 * A173703 A173704 A173705

Keyword

nonn

Author

Jonathan Vos Post, Nov 25 2010

Status

approved