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

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
        p = nextprime(p)
for n in range(12): print(a(n), end=", ") # Michael S. Branicky, Aug 15 2021

Crossrefs

Cf. A232128, A232127, A232126, A232125.

Sequence in context: A143294 A143428 A143385 * A298061 A297984 A298633

Adjacent sequences: A231423 A231424 A231425 * A231427 A231428 A231429

Keyword

nonn,base,more

Author

Michel Marcus and M. F. Hasler, Nov 19 2013

Extensions

a(12)-a(13) from Michael S. Branicky, Aug 15 2021

Status

approved