A116171 Numbers k such that k concatenated with k+2 gives the product of two numbers which differ by 3.

8, 52, 63716866, 48793687600063875363014809897052, 60020753655608135708762056127156, 60446518621981165303188950156776, 71135436903815748345367595855336, 72876856643103028189103298533248, 84570848711413793538075759738752, 85076101372363641092906686735252, 99714785145539288825781952765036

Offset

1,1

Comments

Also numbers k such that k concatenated with k+4 gives the product of two numbers which differ by 1.

If k+2 has d digits, the concatenation is k//k+2 = 10^d*k+k+2 = m*(m+3), therefore 10^d*k+k-8 = (m-2)*(m+5), so there is a large overlap with A116107. - R. J. Mathar, May 22 2026

Links

Robert Israel, Table of n, a(n) for n = 1..36

Example

63716866//63716868 = 79822844 * 79822847, where // denotes concatenation.
63716866//63716870 = 79822845 * 79822846.

Maple

As:= {}: count:= 0:
for m from 2 to 50 do
   acands:= map(t -> rhs(op(t)), [msolve(a*(a+1)=4, 10^m+1)]);
   bcands:= map(t -> t*(t+1) mod 10^m, acands);
   good:= select(t -> bcands[t]>=10^(m-1), [$1..nops(acands)]);
   As:= As union convert(bcands[good], set);
od:
map(t -> t-4, sort(convert(As, list))); # Robert Israel, Mar 18 2026

Crossrefs

Cf. A116099, A116170, A116172, A116112, A116302, A116099, A115428, A116314.

Sequence in context: A359126 A199700 A302865 * A303966 A304928 A305344

Adjacent sequences: A116168 A116169 A116170 * A116172 A116173 A116174

Keyword

nonn,base

Author

Giovanni Resta, Feb 06 2006

Extensions

Edited by N. J. A. Sloane, Apr 13 2007

More terms from Robert Israel, Mar 18 2026

Status

approved