A073682 Prime sum of n-th group of successive primes in A073684.

5, 23, 101, 109, 263, 211, 251, 757, 1367, 941, 2053, 1901, 911, 2347, 1861, 1187, 1249, 1303, 2273, 1433, 1493, 1553, 2777, 2927, 44843, 26699, 65713, 4597, 14159, 8069, 18439, 5197, 8819, 9011, 9277, 9419, 33599, 53381, 6761, 6823, 11497, 7013

Offset

1,1

Comments

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.

Links

Zak Seidov, Table of n,a(n) for n = 1..3000

Zak Seidov, Table of n, A073682(n), A073683(n), A073684(n), A077279(n) for n = 1..3000

Example

a(1)=5 because sum of first two primes 2+3 = 5 is prime;
a(2)=23 because sum of next three primes 5+7+11 = 23 is prime;
a(3)=101 because sum of next five primes 13+17+19+23+29 = 101 is prime.

Prog

(Python)
from itertools import count, islice
from sympy import isprime, nextprime
def agen(): # generator of terms
    s, i, p = 0, 1, 2
    while True:
        while not(isprime(s:=s+p)) or i < 2:
            i, p = i+1, nextprime(p)
        yield s
        s, i, p = 0, 1, nextprime(p)
print(list(islice(agen(), 42))) # Michael S. Branicky, May 23 2025

Crossrefs

Cf. A073683, A073684, A077279.

Sequence in context: A387061 A049674 A077277 * A034958 A229008 A274322

Adjacent sequences: A073679 A073680 A073681 * A073683 A073684 A073685

Keyword

nonn

Author

Amarnath Murthy, Aug 11 2002

Extensions

More terms from Gabriel Cunningham (gcasey(AT)mit.edu), Apr 10 2003

Status

approved