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%I A152607 #12 Jul 13 2022 03:41:00
%S A152607 1,3,7,9,71,73,79,711,713,717,971,973,1111,1113,1117,1119,7111,7113,
%T A152607 7117,9711,9713,11111,11113,11117,11119,71111,71113,71117,97111,97113,
%U A152607 111111,111113,111117,111119,711111,711113,711117,971111
%N A152607 a(1) = 1; thereafter a(n) is always the smallest integer > a(n-1) not leading to a contradiction, such that the concatenation of any two consecutive digits in the sequence is a prime.
%C A152607 Computed by Jean-Marc Falcoz.
%C A152607 Comment from Jean-Marc Falcoz: (Start)
%C A152607 The sequence is infinite since it has the following structure:
%C A152607 9713, 11111, 11113, 11117, 11119, 71111, 71113, 71117, 97111,
%C A152607 97113, 111111, 111113, 111117, 111119, 711111, 711113, 711117, 971111,
%C A152607 971113, 1111111, 1111113, 1111117, 1111119, 7111111, 7111113, 7111117, 9711111,
%C A152607 9711113, 11111111, 11111113, 11111117, 11111119, 71111111, 71111113, 71111117, 97111111,
%C A152607 97111113, 111111111, 111111113, 111111117, 111111119, 711111111, 711111113, 711111117, 971111111,
%C A152607 971111113, 1111111111, 1111111113, 1111111117, 1111111119, 7111111111, 7111111113, 7111111117, 9711111111,
%C A152607 9711111113, ... (End)
%H A152607 Eric Angelini, <a href="http://www.cetteadressecomportecinquantesignes.com/ConsecDig.htm">Chiffres consecutifs dans quelques suites</a>
%H A152607 Eric Angelini, <a href="/A152136/a152136.pdf">Chiffres consecutifs dans quelques suites</a> [Cached copy, with permission]
%o A152607 (Python)
%o A152607 from itertools import count, islice
%o A152607 def cgen(seed, digits, geq="0"): # numbers satisfying the condition
%o A152607     allowed = {"1": "1379", "3": "17", "7": "139", "9": "7"}
%o A152607     if digits == 1:
%o A152607         yield from (c for c in allowed[seed] if c >= geq); return
%o A152607     for f in (c for c in allowed[seed] if c >= geq):
%o A152607         yield from (f + r for r in cgen(f, digits-1))
%o A152607 def nextc(k): # next element of cgen greater than k
%o A152607     s = str(k)
%o A152607     for d in count(len(s)):
%o A152607         geq = s[0] if d == len(s) else "0"
%o A152607         for c in map(int, cgen(s[-1], d, geq=geq)):
%o A152607             if c > k: return c
%o A152607 def agen():
%o A152607     an = 1
%o A152607     for n in count(1): yield an; an = nextc(an)
%o A152607 print(list(islice(agen(), 40))) # _Michael S. Branicky_, Jul 12 2022
%o A152607 (Python) # alternate using pattern from comments
%o A152607 from itertools import count, islice
%o A152607 def agen():
%o A152607     yield from [1, 3, 7, 9, 71, 73, 79, 711, 713, 717, 971]
%o A152607     for i in count(0):
%o A152607         i1 = "1"*i
%o A152607         yield from map(int, ("97"+i1+"3", i1+"1111", i1+"1113", i1+"1117", i1+"1119", "7111"+i1, "711"+i1+"3", "711"+i1+"7", "9711"+i1))
%o A152607 print(list(islice(agen(), 40))) # _Michael S. Branicky_, Jul 12 2022
%Y A152607 Cf. A158652, A152604-A152609. See A152136 for another version.
%K A152607 nonn,base
%O A152607 1,2
%A A152607 _N. J. A. Sloane_, Sep 23 2009

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