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

1,1

Links

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

Formula

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

Example

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A124966-A124970.

Sequence in context: A158803 A340050 A051780 * A272635 A105448 A336007

Adjacent sequences: A124968 A124969 A124970 * A124972 A124973 A124974

Keyword

nonn

Author

Artur Jasinski, Nov 14 2006

Extensions

Corrected and extended by Ray Chandler, Nov 30 2006

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

Status

approved