A316943 Numbers k that are a substring of (k-1)*k*(k+1).

32, 50, 56, 500, 782, 792, 1165, 5000, 5111, 7484, 8933, 23927, 31623, 46271, 50000, 53257, 64164, 65137, 66995, 78313, 86181, 98442, 316228, 405927, 500000, 803633, 1939055, 1969394, 2133896, 2438170, 3162278, 4039599, 4150015, 5000000, 5354867, 5887042, 6249997

Offset

1,1

Comments

Any number of the form 5*10^m, with m>0, is part of the sequence.

Links

Paolo P. Lava, Table of n, a(n) for n = 1..74

Example

31*32*33 = 32736 and 32 is a substring, so it is in the sequence.
5110*5111*5112 = 133511177520 and 5111 is a substring, so it is in the sequence.

Maple

P:=proc(q) local k, n; for n from 1 to q do
for k from 1 to ilog10((n-1)*n*(n+1))-ilog10(n)+1 do
if n=trunc((n-1)*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[10^5], SequenceCount @@ Map[IntegerDigits, {(# - 1) # (# + 1), #}] > 0 &] (* Michael De Vlieger, Jul 20 2018 *)
Select[Range[63*10^5], SequenceCount[IntegerDigits[#^3-#], IntegerDigits[#]]>0&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Dec 26 2018 *)

Crossrefs

Cf. A305670, A316263.

Sequence in context: A259765 A256521 A037008 * A099048 A176542 A346917

Adjacent sequences: A316940 A316941 A316942 * A316944 A316945 A316946

Keyword

nonn,base

Author

Paolo P. Lava, Jul 17 2018

Status

approved