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%I #10 Jun 17 2022 17:05:25
%S 0,1,3,6,14,15,26,68,75,129,158,186,249,759,1616,1827,2268,2679,4543,
%T 6072,6675,7294,13512,16146,27871,112640,116339,152889,161727,239533,
%U 260487,404161,670038,685744,767718,973504,2313206,6250177,6977617
%N Numbers n such that A002113(n) is a triangular number.
%C Indices of triangular numbers in the sequence of palindromes.
%e A002113(26) = 171 is a triangular number, so 26 is a term.
%t Join[{0},Flatten[Position[Select[Range[10^7],PalindromeQ],_?(OddQ[Sqrt[ 8#+1]]&)]]] (* The program generates the first 22 terms of the sequence. *) (* _Harvey P. Dale_, Jun 17 2022 *)
%o (ARIBAS) var c,n,m:integer; end; begin c:=0; for n:=0 to 100000000 do if n = intreverse(n) then m:=floor(sqrt(2*n)); if m*(m+1) div 2 = n then write(c,","); end; inc(c); end; end; end;
%o (PARI) {c=0;for(n=0,10000000,k=n;r=0;while(k>0,d=divrem(k,10);k=d[1];r=10*r+d[2]); if(n==r,m=sqrtint(2*n);if(m*(m+1)/2==n,print1(c,","));c++))}
%Y Cf. A000217, A002113, A003098, A008509.
%K nonn,base
%O 1,3
%A _Klaus Brockhaus_, Nov 27 2004
%E a(24) to a(38) from _Klaus Brockhaus_, Oct 05 2005