A231426 - OEIS

A231426

Least prime such that at most n digits may be appended to the right, preserving primality at each step.

53, 11, 97, 17, 71, 43, 13, 2, 19, 103, 409, 1457011, 2744903797, 5232781111

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OFFSET

0,1

LINKS

Table of n, a(n) for n=0..13.

FORMULA

a(n) is the least prime p=prime(k) such that A232128(p) (= A232127(k)) = n.

If a(n) = p, then a(n) = floor(A232129(p)/10^A232128(p)).

A232125(n) <= (a(n)+1)*10^n - 1. - Michael S. Branicky, Aug 15 2021

EXAMPLE

a(7) = 2 is the least prime which starts several sequences of 1+7 primes, e.g., (2, 23, 239, 2393, ..., 23399339) and others leading at most to 29399999 = A232129(2), where a digit is appended 7 times to yield a prime after each step, while it is not possible in any of the "branches" to append one more digit to the last term, preserving primality.

PROG

(Python)

from sympy import isprime, nextprime

def a(n):

p = 2

while True:

extends, reach = -1, {p}

while len(reach) > 0:

candidates = (int(str(e)+d) for d in "1379" for e in reach)

reach1 = set(filter(isprime, candidates))

extends, reach = extends + 1, reach1

if extends == n: return p