A392157 a(n) is the number of prime-to-prime deletion paths from prime(n) to a one-digit prime, where at each step exactly one decimal digit is removed and the resulting number, interpreted without leading zeros, is prime.

1, 1, 1, 1, 0, 1, 1, 0, 2, 1, 1, 2, 0, 1, 1, 2, 1, 0, 1, 1, 2, 1, 1, 0, 1, 0, 2, 2, 0, 2, 1, 2, 4, 1, 0, 0, 1, 1, 2, 4, 2, 0, 0, 1, 2, 0, 0, 4, 0, 2, 4, 3, 0, 0, 0, 2, 1, 1, 0, 0, 3, 3, 3, 2, 2, 4, 2, 4, 3, 0, 2, 1, 3, 4, 3, 1, 0, 3, 0, 0, 0, 0, 2, 2, 1, 2, 0, 1

Offset

1,9

Links

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

Formula

a(n) <= floor(log_10(prime(n)) + 1)!.

a(n) = 0 if prime(n) is not a term of A118950.

Example

a(1) = 1 since prime(1) = 2 is already a one-digit prime.
a(27) = 2 since prime(27) = 103. Deleting one digit yields 03, 13, 10; ignoring leading zeros and nonprimes, the prime continuations are 3 and 13. From 13, a further deletion gives 3; from 3, the path already terminates. Hence there are two prime endpoints in total (both 3).
a(33) = 4 since prime(33) = 137. Deleting one digit yields 37, 17, 13, all prime. Deleting again gives {3, 7} from 37, {1, 7} from 17, and {1, 3} from 13; among these, the primes are 3, 7, 7, 3, for a total of four.
a(36) = 0 since prime(36) = 151. Deleting one digit yields 51, 11, 15; only 11 is prime. Deleting again from 11 yields 1 and 1, which are not prime, so no path reaches a one-digit prime.

Maple

A392157 := proc(n) local b, i, k, l, p; b := proc(x) local d, j; d := ListTools:-Reverse(convert(x, 'base', 10)); `if`(nops(d) = 1, x, [seq(select(isprime, map(k -> foldl((x, y) -> 10*x + y, 0, op(k)), [seq(subsop(j = NULL, d), j = 1 .. nops(d))])))]); end proc; p := [ithprime(n)]; l := length(op(p)); while 1 < l do k := [seq(op(b(i)), i in p)]; p := k; l := l - 1; end do; return nops(select(isprime, p)); end proc: seq(A392157(n), n = 1 .. 88);

Crossrefs

Cf. A000040, A118950, A392156.

Sequence in context: A374318 A109066 A079066 * A157188 A329257 A173266

Adjacent sequences: A392154 A392155 A392156 * A392158 A392159 A392160

Keyword

nonn,base

Author

Felix Huber, Jan 20 2026

Status

approved