Search: id:A118711
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%I A118711
%S A118711 1,13,61,82,898,2962,2989,9133,20077,20653,28669,29266,35581,35842,
%T A118711 37501,99133,236674,286717,424621,424957,821698,941650,1704301,1722370,
%U A118711 2978413,3328258,4494466,10022317,40392829,49870141,50668882,53933053
%N A118711 Integers n such that the n-th triangular number t_n has all its base 
               12 digits contained in {1,5,7,11}.
%C A118711 In base 12 all primes greater than 3 end in the digits 1, 5, 7, E, where 
               X is 10 and E is 11. They are the digits that satisfies GCD(d,12)=1.
%C A118711 The sequence in base 12 is: 1, 11, 51, 6X, 62X, 186X, 1891, 5351, E751, 
               EE51, 14711, 14E2X, 18711, 188XX, 19851, 49451, E4E6X, 119E11, 185891, 
               185E11, 33762X, 394E2X, 6X2351, 6E08XX, EE7751, 11460XX, 1608E6X, 
               3433E51, 1163E591, 14850051, 14E7632X, 1608E311, 18331451, 1870E191, 
               1974E311, ..., . Note that all elements end in 1 or X. The corresponding 
               triangular numbers after the first end in the digits 17 or 77, but 
               not respectively.
%F A118711 a(n)=m if the m-th triangular number t_m=m*(m+1)/2 has its base 12 digits 
               contained in {1,5,7,11}.
%e A118711 a(4)=82=6X since the triangular number t=82*(82+1)/2=3403=1E77.
%p A118711 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;
%t A118711 fQ[n_] := Union@ Join[{1, 5, 7, 11}, IntegerDigits[n(n + 1)/2, 12]] == 
               {1, 5, 7, 11}; Do[ If[fQ@n, AppendTo[lst, n]], {n, 10^8}] (* Robert 
               G. Wilson v *)
%Y A118711 Cf. A000217, A119033, A119034.
%Y A118711 Sequence in context: A146764 A145474 A002647 this_sequence A028874 A087106 
               A142402
%Y A118711 Adjacent sequences: A118708 A118709 A118710 this_sequence A118712 A118713 
               A118714
%K A118711 nonn,base
%O A118711 1,2
%A A118711 Walter Kehowski (wkehowski(AT)cox.net), May 24 2006
%E A118711 Edited and extended a(23)-a(32) by Robert G. Wilson v (rgwv(at)rgwv.com), 
               Jun 20 2006

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