A381126 Primes that are the concatenation of prime(p) and p where p is a prime.

53, 6719, 15737, 587107, 1297211, 1823281, 1913293, 3067439, 3593503, 3943547, 4397599, 5503727, 5651743, 6353827, 6361829, 6823877, 7109911, 7283929, 7523953, 85131061, 85271063, 87611093, 88071097, 104331277, 125031493, 128411531, 130031549, 133311583, 141071663

Offset

1,1

Links

Table of n, a(n) for n=1..29.

Wikipedia, Super-prime

Example

1297211 is a term since it is prime and is the concatenation of prime(p) = 1297 and p = 211.

Maple

f:= p-> (h-> `if`(andmap(isprime, [p, h]), h, [][]))(parse(cat(ithprime(p), p))):
map(f, [$1..2000])[];  # Alois P. Heinz, Feb 15 2025

Prog

(Python)
from sympy import isprime, primerange, prime
def a(limit: int) -> list[int]:
    result: list[int] = []
    for p in primerange(2, limit):
        pth_prime = prime(p)
        rc_val = int(f"{pth_prime}{p}")
        if isprime(rc_val):
            result.append(rc_val)
    return result
print(a(1700))
(PARI) a381126(limit) = {forprime (p=2, limit, my(pd=digits(p), ppd=digits(prime(p)), pc=fromdigits(concat(ppd, pd))); if(isprime(pc), print1(pc, ", ")))};
a381126(2000) \\ Hugo Pfoertner, Feb 14 2025

Crossrefs

Subsequence of A084669.

Cf. A006450, A084667, A229814.

Sequence in context: A370294 A088784 A104820 * A093253 A293080 A267950

Adjacent sequences: A381123 A381124 A381125 * A381127 A381128 A381129

Keyword

nonn,base

Author

Maja Gwozdz, Feb 14 2025

Status

approved