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 A347424 Digitally delicate truncatable primes: every suffix is prime, changing any one decimal digit always produces a composite number, except the first to zero. 1
 7810223, 19579907, 909001523, 984960937, 78406036607, 90124536947, 99020400307, 190002706337, 393086079907, 500708906197, 509000702017, 600180367883, 780430098443, 3534900290107, 5046024021013, 6006006800743, 6009000432797, 9001924501223, 12090900340283 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS These prime numbers are both: - digitally delicate primes (also called weakly prime numbers) A158124: changing any one decimal digit always produces a composite number, with restriction that first digit may not be changed to a 0 (that means no change of the number of significant digits from its original value). - left-truncatable primes A033664: every suffix is prime, means repeatedly deleting the most significant digit gives a prime at every step until a single-digit prime remains. LINKS Michael S. Branicky, Table of n, a(n) for n = 1..9175 (all terms with <= 29 digits) PROG (Python) from sympy import isprime, primerange def is_digitally_delicate(p): s = str(p) for i in range(len(s)): for d in "0123456789": if d != s[i] and not (i == int(d) == 0): if isprime(int(s[:i] + d + s[i+1:])): return False return True def A033664gen(maxdigits): yield from [2, 3, 5, 7] primestrs, digits, d = ["2", "3", "5", "7"], "0123456789", 1 while len(primestrs) > 0 and d < maxdigits: cands = (d+p for p in primestrs for d in "0123456789") primestrs = [c for c in cands if c[0] == "0" or isprime(int(c))] yield from sorted(map(int, (p for p in primestrs if p[0] != "0"))) d += 1 def afind(maxdigits): for p in A033664gen(maxdigits): if is_digitally_delicate(p): print(p, end=", ") afind(12) # Michael S. Branicky, Sep 01 2021 CROSSREFS Cf. A158124, A033664. Sequence in context: A124416 A320516 A319809 * A214194 A205657 A206186 Adjacent sequences: A347421 A347422 A347423 * A347425 A347426 A347427 KEYWORD nonn,base AUTHOR Marc Morgenegg, Sep 01 2021 EXTENSIONS a(3)-a(4) from Amiram Eldar, Sep 01 2021 a(5)-a(19) from Michael S. Branicky, Sep 01 2021 STATUS approved

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Last modified February 22 12:20 EST 2024. Contains 370255 sequences. (Running on oeis4.)