A116309 Numbers k such that k*(k+3) gives the concatenation of two numbers m and m+3.

40, 58, 32262232, 67737766, 79321056, 3341093417798787499093, 3861488851737861033961, 4747922651210186579787, 5252077348789813420211, 6138511148262138966037, 6658906582201212500905, 7232275368591793618231

Offset: 1

Author

Giovanni Resta, Feb 06 2006

Keywords

• nonn
• base

Examples

			79321056 * 79321059 = 62918301//62918304, where // denotes concatenation.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..67
• Robert Israel, Maple program used to obtain b-file

Crossrefs

Cf. A116112, A116302, A116308, A116310, A116316.

Programs

Maple

As:= {}:
for m from 2 to 62 do
   acands:= map(t -> rhs(op(t)), [msolve(a*(a+3)=3, 10^m+1)]);
   bcands:= map(t -> t*(t+3) mod 10^m, acands);
   good:= select(t -> bcands[t]>=10^(m-1), [$1..nops(acands)]);
   As:= As union convert(acands[good],set);
od:
sort(convert(As,list)); # Robert Israel, Aug 20 2019