A059932 a(n) is formed by concatenating the next prime(n) primes.

23, 5711, 1317192329, 31374143475359, 6167717379838997101103107, 109113127131137139149151157163167173179, 181191193197199211223227229233239241251257263269271, 277281283293307311313317331337347349353359367373379383389, 397401409419421431433439443449457461463467479487491499503509521523541

Offset

1,1

Comments

Original name: Prime groupings.

The n-th term of the sequence is determined by grouping the prime numbers according to the natural order of primes themselves, e.g. the first prime is 2 so group the first two primes 2 and 3. Second prime is 3 so group the next 3 primes 5, 7 and 11, etc.

a(47) has 1055 digits. - Michael S. Branicky, Dec 30 2025

Links

Michael S. Branicky, Table of n, a(n) for n = 1..46

Formula

a(n) = A000040(A007504(n-1)+1)|..|A000040(A007504(n)) where | denotes concatenation. - Michael S. Branicky, Dec 30 2025

Prog

(Python)
from sympy import nextprime
from itertools import islice
def agen(): # generator of terms
    p, q, s = 2, 2, []
    while True:
        while len(s) < p:
            s += [str(q)]
            q = nextprime(q)
        yield int("".join(s))
        p, s = nextprime(p), []
print(list(islice(agen(), 9))) # Michael S. Branicky, Dec 30 2025
(Python)
from sympy import prime, primerange
def a(n):
    p = prime(n)
    s = sum(primerange(1, p))
    return int("".join(map(str, primerange(prime(s+1), prime(s+p)+1))))
print([a(n) for n in range(1, 10)]) # Michael S. Branicky, Dec 30 2025

Crossrefs

Cf. A000040, A007504, A043347.

Sequence in context: A286706 A366585 A134801 * A045735 A233109 A193430

Adjacent sequences: A059929 A059930 A059931 * A059933 A059934 A059935

Keyword

easy,nonn,base

Author

Jason Earls, Mar 01 2001

Extensions

Offset and name changed by and a(8) onward from Michael S. Branicky, Dec 30 2025

Status

approved