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

1,3

Comments

Indices of triangular numbers in the sequence of palindromes.

Links

Table of n, a(n) for n=1..39.

Example

A002113(26) = 171 is a triangular number, so 26 is a term.

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 *)

Prog

(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;
(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++))}

Crossrefs

Cf. A000217, A002113, A003098, A008509.

Sequence in context: A322183 A295292 A053365 * A342103 A084168 A075390

Adjacent sequences: A101031 A101032 A101033 * A101035 A101036 A101037

Keyword

nonn,base

Author

Klaus Brockhaus, Nov 27 2004

Extensions

a(24) to a(38) from Klaus Brockhaus, Oct 05 2005

Status

approved