A124971 Numbers n which can be expressed as the ordered sum of 3 squares in 2 or more different ways and such that n+1 has the same property.

17, 25, 26, 33, 49, 50, 53, 61, 65, 68, 72, 73, 74, 81, 82, 85, 89, 97, 98, 99, 100, 101, 104, 105, 106, 107, 108, 109, 113, 116, 117, 121, 122, 125, 129, 130, 131, 136, 137, 138, 144, 145, 146, 149, 152, 153, 154, 157, 161, 164, 165, 169, 170, 173, 177, 178

Offset: 1

Author

Artur Jasinski, Nov 14 2006

Keywords

• nonn

Examples

			a(1)=17 because 17=3^2+2^2+2^2 = 4^2+1^2+0^2 and a(1)+1= 18=3^2+3^2+0^2 = 4^2+1^2+1^2
		

Links

• R. J. Mathar, Table of n, a(n) for n = 1..6598

Crossrefs

Cf. A124966-A124970.

Programs

Mathematica

Select[Range[200], Length@PowersRepresentations[#, 3, 2] > 1 && Length@PowersRepresentations[# + 1, 3, 2] > 1 &] (* Ray Chandler, Oct 31 2019 *)

PARI

isCnt3sqr(n)={ local(cnt=0,z2) ; for(x=0,floor(sqrt(n)), for(y=x,floor(sqrt(n-x^2)), z2=n-x^2-y^2 ; if( z2>=y^2 && issquare(z2), cnt++ ; ) ; if(cnt >=2, return(1) ) ; ) ; ) ; return(0) ; } isA124971(n)= { return( isCnt3sqr(n) && isCnt3sqr(n+1)) ; } { for(n=1,200, if( isA124971(n), print1(n,", ") ; ) ; ) ; } \\ R. J. Mathar, Nov 29 2006

Formula

A000164(n)>=2 and A000164(n+1)>=2. - R. J. Mathar, Nov 29 2006

Extensions

Corrected and extended by Ray Chandler, Nov 30 2006

Corrected and extended by R. J. Mathar, Nov 29 2006