|
|
A118706
|
|
Triangular numbers whose digits in base 12 are contained in {1,5,7,11}.
|
|
0
|
|
|
1, 91, 1891, 3403, 403651, 4388203, 4468555, 41710411, 201553003, 213283531, 410970115, 428264011, 633021571, 642342403, 703181251, 4913725411, 28007409475, 41103462403, 90151709131, 90294438403, 337594212451
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
In base 12 all primes greater than 3 end in a 1, 5, 7, or E, where X is 10 and E is eleven. In base 12 the sequence is 1, 77, 1117, 1E77, 175717, 1577577, 15E5E77, 11E75E77, 575EE577, 5E517E77, E5771E17, EE511E77, 157EE7E17, 15E151E17, 1775E1717, E5171E117, 551775E717, 7E71571E17, 1557E75EE77, 155EE511E17, 55517751117, 71E11E71E77. Note that all elements after the first either end in 17 or 77. In base 12 the n such that t=n(n+1)/2 end in the digits 1 or X, but not respectively.
|
|
LINKS
|
|
|
FORMULA
|
a(n)=t if t is the n-th triangular number such that S subset {1,5,7,11}, where S is the set of digits of t in base 12.
|
|
EXAMPLE
|
a(4)=3403=1E77 in base 12.
|
|
MAPLE
|
L:=[]: pd:={1, 5, 7, 11}: for w to 1 do for n from 1 to 10^6 do t:=n*(n+1)/2; lod:=convert(t, base, 12); sod:=convert(lod, set); if sod subset pd then L:=[op(L), [n, t]] fi; od od; L;
|
|
MATHEMATICA
|
Select[Accumulate[Range[822000]], SubsetQ[{1, 5, 7, 11}, IntegerDigits[ #, 12]]&] (* Harvey P. Dale, Oct 18 2019 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,base
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|