A322571 Positive integers A270710(k) (= (k+1)*(3*k-1)) which have only 1 or 2 different digits in base 10.

4, 15, 32, 55, 84, 119, 455, 799, 900, 3332, 3535, 7007, 8855, 244244, 333332, 335335, 400404, 445444, 555559, 666464, 799799, 1999199, 3303300, 33333332, 33353335, 3333333332, 3333533335, 333333333332, 333335333335, 700007077007, 33333333333332, 33333353333335, 3333333333333332, 3333333533333335

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, A018885 (in case of squares), A213516 (in case of triangular numbers), A270710, A322570, A323639.

Programs

Magma

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

Mathematica

Select[Table[(n+1)(3n-1),{n,3334*10^4}],Count[DigitCount[#],0]>7&] (* Harvey P. Dale, Jun 12 2022 *)

PARI

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

Formula

a(n) = A270710(A322570(n)).

For k > 0, A002277(2*k) - 1 is a term.