A153874 Numbers n = abc...k such that a^2*b^2*c^2*...k^2 - 1 = n.

143, 323, 11663

Offset: 1

Author

Vikram Pandya, Jan 03 2009

Keywords

• base
• nonn
• fini
• full
• bref

Examples

			1) 143 = 1^2 * 4^2 * 3^2 - 1 = 1 * 16* 9 - 1. 2) 323 = 3^2 * 2^2 * 3^2 - 1 = 9 * 4 * 9 - 1. 3) 1663 = 1^2 * 1^2* 6^2 * 6^2 * 3^2 - 1 = 1 * 1 * 36 * 36 * 9 - 1.
		

Programs

Mathematica

Select[Range[12000],#==Times@@(IntegerDigits[#]^2)-1&] (* Harvey P. Dale, Feb 06 2022 *)

PARI

n=1;while(n!=10^16,n+=1;j=n^2-1;k=1;while(j!=0,k=k*(j%10)^2;j=floor(j/10));if(k-1==n^2-1,print(n^2-1)))

Extensions

Edited by N. J. A. Sloane, Jan 03 2009