The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A234336 Triangular numbers t such that both distances from t to two nearest squares are perfect squares. 1
 0, 1, 45, 153, 325, 10440, 1385280, 2530125, 145462096, 253472356000, 896473314291600, 18598323060963360, 4923539323344237960, 27021247523935843321, 1779312917089890560241, 2355054824151326520405, 21328127890911040269960, 124797500891024855239125 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Triangular numbers in A234334. Except a(1)=0, a(n) are triangular numbers t such that both t-x and y-t are perfect squares, where x and y are two nearest to k squares: x < t <= y. The sequence of k's such that triangular(k) is in A234334 begins: 0, 1, 9, 17, 25, 144, 1664, 2249, 17056, 712000, ... LINKS Table of n, a(n) for n=1..18. EXAMPLE Triangular(9) = 45 is in the sequence because both 45-36=9 and 49-45=4 are perfect squares, where 36 and 49 are the two squares nearest to 45. PROG (C) #include #include typedef unsigned long long U64; U64 isSquare(U64 a) { U64 r = sqrt(a); return r*r==a; } int main() { for (U64 i=0; i<(1ULL<<32); ++i) { U64 n = i*(i+1)/2, r = sqrt(n); if (r*r==n && n) --r; if (isSquare(n-r*r) && isSquare((r+1)*(r+1)-n)) printf("%llu, ", n); } return 0; } CROSSREFS Cf. A000217, A000290, A229909, A234334. Sequence in context: A044758 A053743 A347874 * A173371 A288669 A305069 Adjacent sequences: A234333 A234334 A234335 * A234337 A234338 A234339 KEYWORD nonn AUTHOR Alex Ratushnyak, Dec 23 2013 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 8 21:25 EDT 2024. Contains 375759 sequences. (Running on oeis4.)