A117960 - OEIS

%I #27 Sep 24 2024 17:38:29

%S 1,3,15,55,91,153,171,351,595,1711,1953,5151,5995,9591,11175,11935,

%T 15753,15931,17391,17955,31375,33153,35511,73153,153735,171991,173755,

%U 193131,193753,371953,399171,513591,551775,559153,571915,791911,917335,939135,1335795

%N Triangular numbers with only odd digits.

%H Jon E. Schoenfield, <a href="/A117960/b117960.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 terms from Alois P. Heinz)

%F Intersection of A000217 and A014261. - _M. F. Hasler_, Nov 20 2021

%p b:= proc(n) option remember; local k; for k from

%p       1+`if`(n=1, 0, b(n-1)) while 0=mul(irem(i, 2),

%p       i=convert(k*(k+1)/2, base, 10) ) do od; k

%p     end:

%p a:= n-> (t-> t*(t+1)/2)(b(n)):

%p seq(a(n), n=1..50);  # _Alois P. Heinz_, Jul 12 2015

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

%o (PARI) select( {is_A117960(n)=is_A000217(n)&&is_A014261(n)}, [2*n+1|n<-[0..99999]]) \\ _M. F. Hasler_, Nov 20 2021

%o (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

%o (Python)

%o from itertools import islice, count

%o def A117960(): return filter(lambda n: set(str(n)) <= {'1','3','5','7','9'}, (m*(m+1)//2 for m in count(0)))

%o A117960_list = list(islice(A117960(),20)) # _Chai Wah Wu_, Nov 22 2021

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

%K base,nonn

%O 1,2

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

%E Some terms corrected by _Alois P. Heinz_, Jul 12 2015