A392156 a(n) is the number of distinct primes obtainable by inserting exactly one decimal digit into the decimal representation of prime(n) (at any position, including before the first digit or after the last), with the resulting number required to have no leading zero.

2, 8, 2, 8, 10, 10, 10, 12, 8, 6, 7, 10, 10, 7, 8, 8, 7, 10, 9, 7, 7, 8, 9, 5, 10, 15, 10, 6, 15, 12, 11, 12, 9, 5, 11, 10, 7, 8, 12, 9, 10, 10, 8, 10, 11, 10, 12, 9, 10, 12, 8, 10, 8, 8, 9, 8, 10, 12, 10, 9, 11, 10, 9, 11, 5, 9, 10, 10, 9, 8, 8, 8, 14, 8, 9, 8

Offset

1,1

Links

Felix Huber, Table of n, a(n) for n = 1..10000

Example

The a(10) = 6 primes obtainable from prime(10) = 29 are 229, 239, 269, 293, 829 and 929.

Maple

A392156 := proc(n) local i, j, k, l, p; p := ListTools:-Reverse(convert(ithprime(n), 'base', 10)); k := nops(p); l := []; for i from 0 to 9 do for j from 0 to k do if i + j > 0 then l := [op(l), [op(p[1 .. j]), i, op(p[j + 1 .. k])]]; end if; end do; end do; nops(convert(select(isprime, {op(map(z -> foldl((x, y) -> 10*x + y, 0, op(z)), l))}), set)); end proc: seq(A392156(n), n = 1 .. 76);

Prog

(Python)
from sympy import isprime, prime
def a(n):
    s = str(prime(n))
    return len(set(p for i in range(len(s)+1) for d in "0123456789"[int(i==0):] if isprime(p:=int(s[:i]+d+s[i:]))))
print([a(n) for n in range(1, 77)]) # Michael S. Branicky, Jan 25 2026

Crossrefs

Cf. A000040, A068164, A125001, A304244, A389720, A389721, A392157.

Sequence in context: A286309 A010466 A086396 * A195844 A388626 A222828

Adjacent sequences: A392153 A392154 A392155 * A392157 A392158 A392159

Keyword

nonn,base

Author

Felix Huber, Jan 20 2026

Status

approved