login
Numbers with consecutive positive decimal digits after the digits are sorted.
2

%I #37 Aug 04 2022 15:03:51

%S 1,2,3,4,5,6,7,8,9,12,21,23,32,34,43,45,54,56,65,67,76,78,87,89,98,

%T 123,132,213,231,234,243,312,321,324,342,345,354,423,432,435,453,456,

%U 465,534,543,546,564,567,576,645,654,657,675,678,687,756,765,768,786,789,798,867,876,879,897,978,987

%N Numbers with consecutive positive decimal digits after the digits are sorted.

%C The last term is a(462331) = 987654321.

%C Observation: the number of terms mentioned above is also A014145(9). Also the sum of the 9th row in the triangle A288777.

%C It appears that the number of terms with k digits in this sequence is also A288777(9,k), k>=1.

%H Michael S. Branicky, <a href="/A288528/b288528.txt">Table of n, a(n) for n = 1..10000</a>

%o (Python)

%o def ok(n): return "".join(sorted(str(n))) in "123456789"

%o print([k for k in range(999) if ok(k)]) # _Michael S. Branicky_, Aug 04 2022

%o (Python) # alternate for generating full sequence instantly

%o from itertools import permutations

%o frags = ["123456789"[i:j] for i in range(9) for j in range(i+1, 10)]

%o afull = sorted(int("".join(s)) for f in frags for s in permutations(f))

%o print(afull[:70]) # _Michael S. Branicky_, Aug 04 2022

%Y Subsequence of A215014.

%Y Supersequence of A138141.

%Y Cf. A014145, A033075, A288777.

%K nonn,base,easy,fini

%O 1,2

%A _Omar E. Pol_, Jun 15 2017