A101034 Numbers n such that A002113(n) is a triangular number.
0, 1, 3, 6, 14, 15, 26, 68, 75, 129, 158, 186, 249, 759, 1616, 1827, 2268, 2679, 4543, 6072, 6675, 7294, 13512, 16146, 27871, 112640, 116339, 152889, 161727, 239533, 260487, 404161, 670038, 685744, 767718, 973504, 2313206, 6250177, 6977617
Offset: 1
Examples
A002113(26) = 171 is a triangular number, so 26 is a term.
Programs
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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;
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Mathematica
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 *) -
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++))}
Extensions
a(24) to a(38) from Klaus Brockhaus, Oct 05 2005
Comments