A275170 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.

369, 1649, 3268, 3924, 6550, 12810, 14472, 25268, 27160, 32650, 38050, 65500, 72712, 100905, 144138, 146016, 146100, 164200, 173070, 210811, 236100, 344200, 655000, 1352045, 1461000, 1642000, 1722240, 2361000, 2701540, 3442000, 4008960, 6161465, 6550000, 14610000

Offset

1,1

Comments

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.

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

Links

Paolo P. Lava, Table of n, a(n) for n = 1..50

Example

3*6*9 + 3*69 = 369;
1*6*4*9 + 16*49 + 1*649 = 1649;
1*2*8*1*0 + 1*28*10 + 12*810 + 1*2810 = 12810.

Maple

P:=proc(q) local a, b, c, k, n; for n from 1 to q do c:=0;
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;
c:=c+a; od; if n=c then print(n); fi; od; end: P(10^12);

Crossrefs

Cf. A275171.

Sequence in context: A205730 A251132 A183351 * A205911 A205903 A237844

Adjacent sequences: A275167 A275168 A275169 * A275171 A275172 A275173

Keyword

nonn,base,easy

Author

Paolo P. Lava, Jul 19 2016

Status

approved