A118711 -id:A118711 - cp's OEIS frontend

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

Walter Kehowski, May 24 2006

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.

			a(4) = 3403 = 1E77 in base 12.

Cf. A000217, A118711, A119033, A119034.

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;

Select[Accumulate[Range[822000]],SubsetQ[{1,5,7,11},IntegerDigits[ #,12]]&] (* Harvey P. Dale, Oct 18 2019 *)

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

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

cp's OEIS Frontend

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

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