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
Links
- Jon E. Schoenfield, Table of n, a(n) for n = 1..10000 (first 1000 terms from Alois P. Heinz)
- Shyam Sunder Gupta, Triangular Numbers, Exploring the Beauty of Fascinating Numbers, Springer (2025) Ch. 3, 82-125.
- Al Zimmermann's Programming Contests, Oddly Triangular, September 2022.
Programs
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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 *) -
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
Formula
Extensions
Some terms corrected by Alois P. Heinz, Jul 12 2015
Comments