A118706 Triangular numbers whose digits in base 12 are contained in {1,5,7,11}.

1, 91, 1891, 3403, 403651, 4388203, 4468555, 41710411, 201553003, 213283531, 410970115, 428264011, 633021571, 642342403, 703181251, 4913725411, 28007409475, 41103462403, 90151709131, 90294438403, 337594212451, 443352832075, 1452321801451, 1483280069635, 4435473488491

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

Table of n, a(n) for n=1..25.

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.

a(n) = A000217(A118711(n)). - Amiram Eldar, Aug 02 2024

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

Cf. A000217, A118711, A119033, A119034.

Sequence in context: A254611 A184462 A229518 * A119150 A008394 A332949

Adjacent sequences: A118703 A118704 A118705 * A118707 A118708 A118709

Keyword

nonn,base

Author

Walter Kehowski, May 24 2006

Extensions

a(22)-a(25) from Amiram Eldar, Aug 02 2024

Status

approved