A153980 - OEIS

%I #29 Dec 29 2024 09:30:40

%S 259146,2185871,2191530,20317438,22608949,30512946,33685085,46400839,

%T 81780856,202677438,302561193,694999138,711286401,788309388,

%U 1006626821,1105599276

%N Positive integers k equal to the sum of all the different integers formed by the digits of k (k itself excluded), keeping the order of the digits.

%C a(17) > 2.25*10^9. - _Tyler Busby_, Apr 17 2024

%C a(17) > 5*10^10. - _Michael S. Branicky_, Oct 10 2024

%e Example 1 : 10554 is not in the sequence, because

%e 0+ 1+ 4+ 5+ 10+ 14+ 15+ 54+ 55+ 104+ 105+ 154+ 155+ 554+ 1054+ 1055+ 1554 = 4893 (instead of 10554)

%e Example 2 : 259146 is in the sequence, because

%e 1+ 2+ 4+ 5+ 6+ 9+ 14+ 16+ 21+ 24+ 25+ 26+ 29+ 46+ 51+ 54+ 56+ 59+ 91+ 94+ 96+ 146+ 214+ 216+ 246+ 251+ 254+ 256+ 259+ 291+ 294+ 296+ 514+ 516+ 546+ 591+ 594+ 596+ 914+ 916+ 946+ 2146+ 2514+ 2516+ 2546+ 2591+ 2594+ 2596+ 2914+ 2916+ 2946+ 5146+ 5914+ 5916+ 5946+ 9146+ 25146+ 25914+ 25916+ 25946+ 29146+ 59146 = 259146

%t big = 55000000; seq = {}; i = 1;

%t f[x_] := Union[ Map[FromDigits, Subsets[IntegerDigits[x], {1, Length[IntegerDigits[x]] - 1}]]];

%t While[i < big, If[Total[f[i]] == i, Print[i]; AppendTo[seq, i]]; i++ ];

%t Print[seq]

%o (Python)

%o from itertools import combinations

%o def ok(n):

%o     s, ds, ss = str(n), set(), 0

%o     for d in range(len(s)-1, 0, -1):

%o         for c in combinations(s, d):

%o             t = int("".join(c))

%o             if t not in ds:

%o                 ds.add(t)

%o                 ss += t

%o                 if ss > n:

%o                     return False

%o     return n and ss == n

%o print([k for k in range(10**6) if ok(k)]) # _Michael S. Branicky_, Nov 07 2022

%Y Cf. A065794 (where the integers formed can appear several times).

%K base,nonn,more,changed

%O 1,1

%A _Jean-Marc Falcoz_, Jan 04 2009

%E a(9) and a(10) from _Sean A. Irvine_, Dec 17 2009

%E a(11)-a(16) from _Bert Dobbelaere_, Apr 18 2019

%E Incorrect formula removed by _Robert Israel_, Oct 10 2024