A372207 a(n) is the smallest prime number that is obtained by concatenating 2 consecutive n-digit integers.

23, 1213, 102101, 10021001, 1000810007, 100010100011, 10000241000023, 1000004210000041, 100000002100000003, 10000000081000000009, 1000000000810000000007, 100000000002100000000001, 10000000000021000000000001, 1000000000001010000000000011, 100000000000002100000000000003

Offset

1,1

Comments

It is possible to form primes by concatenating an integer with its successor (A030458), as well as by concatenating an integer with its predecessor (A052089).

Links

Michael S. Branicky, Table of n, a(n) for n = 1..500

Example

a(3) = 102101, since when concatenating 3-digit numbers, the first three numbers obtained, in increasing order, are 100101, 101100, 101102, which are composite, while the next number in the list is 102101, which is prime.

Prog

(Python)
from sympy import isprime
def a(n):
    if n == 1: return 23
    lb, ub = 10**(n-1), 10**n
    for k in range(lb, ub, 2):
        base = k*ub
        for inc in [k-1, k+1]:
            if inc >= lb and isprime(t:=base+inc):
                return t
print([a(n) for n in range(1, 16)]) # Michael S. Branicky, May 19 2024

Crossrefs

Cf. A030458, A052089.

Sequence in context: A340487 A321569 A061063 * A100768 A353143 A201309

Adjacent sequences: A372204 A372205 A372206 * A372208 A372209 A372210

Keyword

nonn,base

Author

Gonzalo Martínez, May 19 2024

Extensions

a(12) and beyond from Michael S. Branicky, May 19 2024

Status

approved