A037050 Numbers n such that product of n with sum of next n consecutive integers is palindromic.

1, 121, 187, 14014

Offset: 1

Author

Patrick De Geest, Jan 04 1999

Keywords

• nonn
• base
• hard
• more

Comments

Also, number n such that n^2*(3*n+1)/2 is palindromic.

No additional terms below 10^10. - Jens Voß, Feb 20 2009

a(5) > 3.7*10^12, if it exists. - Giovanni Resta, Aug 26 2019

Examples

			187 * (188+189+...+373+374) = 187 * 52547 = palindrome 9826289.
		

Crossrefs

Cf. A036659, A037051.

Programs

Maple

A036659 := proc(n) n^2*(3*n+1)/2 ; end: isA002113 := proc(n) local b10,i ; b10 := convert(n,base,10) ; for i from 1 to nops(b10)/2 do if op(i,b10) <> op(-i,b10) then RETURN(false) ; fi ; od ; RETURN(true) ; end: for n from 1 to 1000000 do c := A036659(n) : if isA002113(c) then print(n) ; fi ; od : # R. J. Mathar, Jun 26 2007