cp's OEIS Frontend

A381135 Numbers of the form d_1 d_2 d_3 ... where the sum of their digits multiplied by their digit positions is equal to their number of digits.

%I A381135 #23 Mar 04 2025 23:22:06
%S A381135 1,20,110,300,1010,2100,4000,10010,12000,20100,31000,50000,100010,
%T A381135 111000,200100,220000,301000,410000,600000,1000010,1020000,1101000,
%U A381135 1300000,2000100,2110000,3001000,3200000,4010000,5100000,7000000,10000010,10110000,11001000,12100000
%N A381135 Numbers of the form d_1 d_2 d_3 ... where the sum of their digits multiplied by their digit positions is equal to their number of digits.
%C A381135 The digits for these numbers are 1-indexed.
%C A381135 Numbers k such that A156207(k) = A055642(k).
%H A381135 Michael S. Branicky, <a href="/A381135/b381135.txt">Table of n, a(n) for n = 1..10000</a>
%H A381135 Michael S. Branicky, <a href="/A381135/a381135.py.txt">Python program for OEIS A381135</a>
%e A381135 301000 is a member of this sequence because it has 3*1 + 1*3 = 6 digits.
%o A381135 (Python)
%o A381135 def ok(n): return sum(int(d)*(i+1) for i, d in enumerate(str(n))) == len(str(n))
%o A381135 (Python) # see linked program for a different algorithm
%o A381135 from itertools import count, islice
%o A381135 from sympy.utilities.iterables import partitions
%o A381135 def agen(): # generator of terms
%o A381135     for d in count(1): yield from sorted(int("".join(str(p[k]) if k in p else "0" for k in range(1, d+1))) for p in partitions(d, m=d, k=d) if max(p.values()) < 10 if 1 in p and p[1] != 0)
%o A381135 print(list(islice(agen(), 34))) # _Michael S. Branicky_, Feb 19 2025
%o A381135 (PARI) isok(k) = my(d=digits(k)); sum(i=1, #d, i*d[i]) == #d; \\ _Michel Marcus_, Feb 17 2025
%Y A381135 Cf. A055642, A156207.
%K A381135 nonn,base
%O A381135 1,2
%A A381135 _Leo Crabbe_, Feb 14 2025
%E A381135 More terms from _Michel Marcus_, Feb 17 2025