

A231426


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


1



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

0,1


LINKS



FORMULA

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


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)


CROSSREFS



KEYWORD

nonn,base,more


AUTHOR



EXTENSIONS



STATUS

approved



