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Partition the j digits of n into blocks of k, with 1 <= k <= j-1, starting at right and multiply. Sum of these numbers equals n.
2

%I #22 Aug 06 2016 23:41:33

%S 369,1649,3268,3924,6550,12810,14472,25268,27160,32650,38050,65500,

%T 72712,100905,144138,146016,146100,164200,173070,210811,236100,344200,

%U 655000,1352045,1461000,1642000,1722240,2361000,2701540,3442000,4008960,6161465,6550000,14610000

%N Partition the j digits of n into blocks of k, with 1 <= k <= j-1, starting at right and multiply. Sum of these numbers equals n.

%C Any number of the form 655*10^(k+1), 1461*10^(k+2), 1642*10^(k+2), 2361*10^(k+2), 3442*10^(k+2), with k>=0, belongs to the sequence.

%C The number of partitions of k digits are [j-(j mod k)]/k. If j is not a multiple of k the last partition has j mod k digits. E.g.: the partitions of 3 digits of 1123885 are 123 and 885 plus a partition of one digit, 1 (here j=7 and k=3). - _Paolo P. Lava_, Aug 04 2016

%H Paolo P. Lava, <a href="/A275170/b275170.txt">Table of n, a(n) for n = 1..50</a>

%e 3*6*9 + 3*69 = 369;

%e 1*6*4*9 + 16*49 + 1*649 = 1649;

%e 1*2*8*1*0 + 1*28*10 + 12*810 + 1*2810 = 12810.

%p P:=proc(q) local a,b,c,k,n; for n from 1 to q do c:=0;

%p for k from 1 to ilog10(n) do a:=1; b:=n; while b>0 do a:=a*(b mod 10^k); b:=trunc(b/10^k); od;

%p c:=c+a; od; if n=c then print(n); fi; od; end: P(10^12);

%Y Cf. A275171.

%K nonn,base,easy

%O 1,1

%A _Paolo P. Lava_, Jul 19 2016