A322570 Positive integers k such that A270710(k) (= (k+1)*(3*k-1)) have only 1 or 2 different digits in base 10.

1, 2, 3, 4, 5, 6, 12, 16, 17, 33, 34, 48, 54, 285, 333, 334, 365, 385, 430, 471, 516, 816, 1049, 3333, 3334, 33333, 33334, 333333, 333334, 483048, 3333333, 3333334, 33333333, 33333334, 333333333, 333333334, 3333333333, 3333333334, 33333333333, 33333333334

Offset: 1

Author

Seiichi Manyama, Aug 29 2019

Keywords

• nonn
• base

Links

• Giovanni Resta, Table of n, a(n) for n = 1..50

Crossrefs

Cf. A002277, A016069, A093137, A213517 (in case of triangular numbers), A270710, A322571.

Programs

Magma

[k:k in [1..10000000]| #Set(Intseq((k+1)*(3*k-1))) le 2]; // Marius A. Burtea, Aug 29 2019

Mathematica

Select[Range@ 50000, Length@ Union@ IntegerDigits[3 #^2 + 2 # - 1] <= 2 &] (* Giovanni Resta, Sep 04 2019 *)

PARI

for(k=1, 1e8, if(#Set(digits(3*k^2+2*k-1))<=2, print1(k", ")))

Formula

For k > 0, A002277(k) is a term.

For k >= 0, A002277(k) + 1 (= A093137(k)) is a term.

Extensions

a(35)-a(36) from Jinyuan Wang, Aug 30 2019

a(37)-a(40) from Giovanni Resta, Sep 04 2019