A117960 Triangular numbers with only odd digits.

1, 3, 15, 55, 91, 153, 171, 351, 595, 1711, 1953, 5151, 5995, 9591, 11175, 11935, 15753, 15931, 17391, 17955, 31375, 33153, 35511, 73153, 153735, 171991, 173755, 193131, 193753, 371953, 399171, 513591, 551775, 559153, 571915, 791911, 917335, 939135, 1335795

Offset

1,2

Links

Jon E. Schoenfield, Table of n, a(n) for n = 1..10000 (first 1000 terms from Alois P. Heinz)

Formula

Intersection of A000217 and A014261. - M. F. Hasler, Nov 20 2021

Maple

b:= proc(n) option remember; local k; for k from
      1+`if`(n=1, 0, b(n-1)) while 0=mul(irem(i, 2),
      i=convert(k*(k+1)/2, base, 10) ) do od; k
    end:
a:= n-> (t-> t*(t+1)/2)(b(n)):
seq(a(n), n=1..50);  # Alois P. Heinz, Jul 12 2015

Mathematica

Select[Table[n(n+1)/2, {n, 0, 1650}], ContainsOnly[IntegerDigits[#], {1, 3, 5, 7, 9}]&] (* James C. McMahon, Sep 24 2024 *)

Prog

(PARI) select( {is_A117960(n)=is_A000217(n)&&is_A014261(n)}, [2*n+1|n<-[0..99999]]) \\ M. F. Hasler, Nov 20 2021
(PARI) apply( {A117960_row(n, t=10^n\9, L=List())=forvec(v=vector(n, i, [0, 4]), is_A000217(n=t+fromdigits(v)*2)&&listput(L, n)); L}, [1..6]) \\ row(n) = terms with n digits. Use concat(%) to flatten. - M. F. Hasler, Nov 23 2021
(Python)
from itertools import islice, count
def A117960(): return filter(lambda n: set(str(n)) <= {'1', '3', '5', '7', '9'}, (m*(m+1)//2 for m in count(0)))
A117960_list = list(islice(A117960(), 20)) # Chai Wah Wu, Nov 22 2021

Crossrefs

Cf. A000217 (triangular numbers), A014261 (numbers with only odd digits), A117978.

Sequence in context: A026696 A082708 A093925 * A176288 A119113 A286185

Adjacent sequences: A117957 A117958 A117959 * A117961 A117962 A117963

Keyword

base,nonn

Author

Luc Stevens (lms022(AT)yahoo.com), May 03 2006

Extensions

Some terms corrected by Alois P. Heinz, Jul 12 2015

Status

approved