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A116309 Numbers k such that k*(k+3) gives the concatenation of two numbers m and m+3. 6
40, 58, 32262232, 67737766, 79321056, 3341093417798787499093, 3861488851737861033961, 4747922651210186579787, 5252077348789813420211, 6138511148262138966037, 6658906582201212500905, 7232275368591793618231 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Robert Israel, Table of n, a(n) for n = 1..67

Robert Israel, Maple program used to obtain b-file

EXAMPLE

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

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

CROSSREFS

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

Sequence in context: A100333 A260609 A260602 * A126816 A259061 A344408

Adjacent sequences:  A116306 A116307 A116308 * A116310 A116311 A116312

KEYWORD

nonn,base

AUTHOR

Giovanni Resta, Feb 06 2006

STATUS

approved

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Last modified August 2 18:52 EDT 2021. Contains 346428 sequences. (Running on oeis4.)