A280447 -id:A280447 - cp's OEIS frontend

A280445 Consider a number k and all the possible concatenations of the form k = concat(a,b), with a>0. Take the sum of the products of all the pairs a and b, j = Sum{a*b}. Sequence lists the numbers for which j/k is an integer and produce a new record.

655, 5848, 176594, 25820986, 1394797593315

Offset: 1

Paolo P. Lava, Jan 03 2017

The ratios for a(1)-a(5) are 1, 2, 3, 4, and 7, respectively. a(6) > 10^13. - Giovanni Resta, Jan 05 2017

			655 = concat(6,55) = concat(65,5) and (6*55 + 65*5)/655 = 1;
5848 = concat(5,848) = concat(58,48) = concat(584,8) and (5*848 + 58*48 + 584*8)/5848 = 2; etc.

Cf. A280446, A280447.

P:=proc(q) local a,j,k,n; j:=0; for n from 1 to q do a:=0;
for k from 1 to ilog10(n) do a:=a+(n mod 10^k)*trunc(n/10^k); od;
if type(a/n,integer) then if a/n>j then j:=a/n; print(n); fi; fi; od; end: P(10^9);

a(5) from Giovanni Resta, Jan 05 2017

A280446 Like A065759 but where f(n) = 2*n.

Original entry on oeis.org

5848, 6884, 58480, 68840, 394062, 584800, 688400, 3940620, 5848000, 6884000, 39406200, 58480000, 68840000

Offset: 1

Paolo P. Lava, Jan 03 2017

Numbers of the form 5848*10^k, 6884*10^k, 394062*10^k, with k>=0, belong to the sequence.

			5848 = concat(5*848) = concat(58*48) = concat(584*8) and (5*848 + 58*48 + 584*8) = 11696 = 2*5848.

Cf. A065759, A280445, A280447.

P:=proc(q) local a,k,n; for n from 1 to q do a:=0;
for k from 1 to ilog10(n) do a:=a+(n mod 10^k)*trunc(n/10^k); od;
if a/n=2 then print(n); fi; od; end: P(10^9);

Select[Range[10^6], Function[n, Module[{a = {}, e = IntegerLength@ n - 1, k}, Do[AppendTo[a, # (n - #*10^(e - k)) &@ Floor[n/10^(e - k)]], {k, 0, e - 1}]; Total@ a] == 2 n]] (* Michael De Vlieger, Jan 04 2017 *)

cp's OEIS Frontend

A280445 Consider a number k and all the possible concatenations of the form k = concat(a,b), with a>0. Take the sum of the products of all the pairs a and b, j = Sum{a*b}. Sequence lists the numbers for which j/k is an integer and produce a new record.

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