A316263 Numbers k that are a substring of k*(k-1).

2, 11, 50, 52, 69, 101, 250, 252, 500, 502, 685, 750, 752, 1001, 1250, 3136, 3752, 5000, 5002, 6250, 8752, 10001, 18752, 31250, 46329, 50000, 50002, 68752, 81250, 84168, 100001, 218752, 281250, 297540, 500000, 500002, 718752, 749500, 781250, 1000001, 1638694, 2914261

Offset

1,1

Comments

Any number of the forms 10^m+1, 5*10^m and 5*10^m+2 (m>0) are part of the sequence.

Links

Paolo P. Lava, Table of n, a(n) for n = 1..93

Example

69 * 68 = 4692;
8752 * 8751 = 76588752.

Maple

P:=proc(q) local k, n; for n from 1 to q do
for k from 1 to ilog10(n*(n-1))-ilog10(n)+1 do
if n=trunc(n*(n-1)/10^(k-1)) mod 10^(ilog10(n)+1) then print(n);
break; fi; od; od; end: P(10^8);

Mathematica

Select[Range[3*10^6], SequenceCount[IntegerDigits[#(#-1)], IntegerDigits[ #]]>0&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Apr 06 2020 *)

Crossrefs

Cf. A305670.

Sequence in context: A036996 A262296 A151314 * A342906 A187000 A154415

Adjacent sequences: A316260 A316261 A316262 * A316264 A316265 A316266

Keyword

nonn,base,easy

Author

Paolo P. Lava, Jun 28 2018

Status

approved