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

Author

Jonathan Vos Post, Nov 25 2010

Keywords

• nonn
• changed

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.

Examples

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

Links

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

Crossrefs

Cf. A002049.

Programs

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

Formula

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