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

3, 11, 29, 41, 61, 73, 89, 127, 173, 197, 251, 283, 311, 353, 383, 401, 421, 439, 463, 487, 503, 523, 569, 599, 983, 1153, 1511, 1543, 1601, 1621, 1721, 1741, 1783, 1823, 1871, 1901, 2029, 2239, 2267, 2281, 2311, 2341, 2383, 2447, 2503, 2539, 2551, 2591

Offset: 1

Author

Zak Seidov, Nov 02 2002

Keywords

• nonn

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.

Crossrefs

Cf. A073684, A092285, A073683.

Programs

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 p
        s, i, p = 0, 1, nextprime(p)
print(list(islice(agen(), 48))) # Michael S. Branicky, May 23 2025