A152607 - OEIS

%I #12 Jul 13 2022 03:41:00

%S 1,3,7,9,71,73,79,711,713,717,971,973,1111,1113,1117,1119,7111,7113,

%T 7117,9711,9713,11111,11113,11117,11119,71111,71113,71117,97111,97113,

%U 111111,111113,111117,111119,711111,711113,711117,971111

%N 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 Computed by Jean-Marc Falcoz.

%C Comment from Jean-Marc Falcoz: (Start)

%C The sequence is infinite since it has the following structure:

%C 9713, 11111, 11113, 11117, 11119, 71111, 71113, 71117, 97111,

%C 97113, 111111, 111113, 111117, 111119, 711111, 711113, 711117, 971111,

%C 971113, 1111111, 1111113, 1111117, 1111119, 7111111, 7111113, 7111117, 9711111,

%C 9711113, 11111111, 11111113, 11111117, 11111119, 71111111, 71111113, 71111117, 97111111,

%C 97111113, 111111111, 111111113, 111111117, 111111119, 711111111, 711111113, 711111117, 971111111,

%C 971111113, 1111111111, 1111111113, 1111111117, 1111111119, 7111111111, 7111111113, 7111111117, 9711111111,

%C 9711111113, ... (End)

%H Eric Angelini, <a href="http://www.cetteadressecomportecinquantesignes.com/ConsecDig.htm">Chiffres consecutifs dans quelques suites</a>

%H Eric Angelini, <a href="/A152136/a152136.pdf">Chiffres consecutifs dans quelques suites</a> [Cached copy, with permission]

%o (Python)

%o from itertools import count, islice

%o def cgen(seed, digits, geq="0"): # numbers satisfying the condition

%o     allowed = {"1": "1379", "3": "17", "7": "139", "9": "7"}

%o     if digits == 1:

%o         yield from (c for c in allowed[seed] if c >= geq); return

%o     for f in (c for c in allowed[seed] if c >= geq):

%o         yield from (f + r for r in cgen(f, digits-1))

%o def nextc(k): # next element of cgen greater than k

%o     s = str(k)

%o     for d in count(len(s)):

%o         geq = s[0] if d == len(s) else "0"

%o         for c in map(int, cgen(s[-1], d, geq=geq)):

%o             if c > k: return c

%o def agen():

%o     an = 1

%o     for n in count(1): yield an; an = nextc(an)

%o print(list(islice(agen(), 40))) # _Michael S. Branicky_, Jul 12 2022

%o (Python) # alternate using pattern from comments

%o from itertools import count, islice

%o def agen():

%o     yield from [1, 3, 7, 9, 71, 73, 79, 711, 713, 717, 971]

%o     for i in count(0):

%o         i1 = "1"*i

%o         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 print(list(islice(agen(), 40))) # _Michael S. Branicky_, Jul 12 2022

%Y Cf. A158652, A152604-A152609. See A152136 for another version.

%K nonn,base

%O 1,2

%A _N. J. A. Sloane_, Sep 23 2009