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 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified December 3 05:03 EST 2023. Contains 367531 sequences. (Running on oeis4.)