A069702 - OEIS

%I #17 Aug 29 2018 06:31:43

%S 105,136,210,231,300,406,435,465,561,630,666,703,861,903,1035,2016,

%T 2211,2556,3003,3916,4005,5151,6105,6216,6555,6786,8001,8911,9453,

%U 10011,10153,19900,20100,20910,23005,28203,39903,41905,46665,48205

%N Triangular numbers with internal digits also forming a triangular number.

%C Includes (2*10^(2*k)-10^k-1)/9 for every k, so the sequence is infinite. - _Robert Israel_, Aug 28 2018

%H Giovanni Resta, <a href="/A069702/b069702.txt">Table of n, a(n) for n = 1..1000</a> (first 210 terms from Robert Israel)

%e 3916 is a member as 3916 and 91 both are triangular.

%p filter:= proc(x) local t,m;

%p   t:= floor(x/10);

%p   m:= ilog10(t);

%p   t:= t - floor(t/10^m)*10^m;

%p   issqr(8*t+1)

%p end proc:

%p select(filter, [seq(x*(x+1)/2,x=14..1000)]); # _Robert Israel_, Aug 28 2018

%t s=Select[Range[14, 400], IntegerQ[Sqrt[1+8FromDigits[Drop[Drop[IntegerDigits[ #(#+1)/2], 1], -1]]]]&]; s(s+1)/2

%Y Cf. A077366.

%K base,nonn

%O 1,1

%A _Amarnath Murthy_, Apr 06 2002

%E Edited by _Dean Hickerson_, Apr 09 2002

%E Edited by _Robert Israel_, Aug 28 2018