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Comment from Jean-Marc Falcoz: (Start) The sequence is infinite since it has the following structure:

The sequence is infinite since it has the following structure:

9711111113, ... (End)

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

print(list(islice(agen(), 440))) # Michael S. Branicky, Jul 12 2022

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

if digits == 1: yield from allowed[seed]; return

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

for f in (c for c in allowed[seed]: yield from (f + r for r in cgen(f, digits-1) if c >= geq):

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

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

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

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

print(list(islice(agen(), 404))) # Michael S. Branicky, Jul 12 2022

print(list(islice(agen(), 40))) # Michael S. Branicky, Jul 12 2022

(Python) # alternate using pattern from comments

from itertools import count, islice

def agen():

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

for i in count(0):

i1 = "1"*i

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))

(Python)

from itertools import count, islice

def cgen(seed, digits): # generator of numbers satisfying the condition

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

if digits == 1: yield from allowed[seed]; return

for f in allowed[seed]: yield from (f + r for r in cgen(f, digits-1))

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

s = str(k)

for d in count(len(s)):

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

if c > k: return c

def agen():

an = 1

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

print(list(islice(agen(), 40))) # Michael S. Branicky, Jul 12 2022

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

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editing