A267431 Indices of Catalan numbers that are not of the form x^2 + y^2 + z^2 where x, y and z are integers.

10, 24, 37, 43, 46, 48, 49, 51, 69, 87, 96, 97, 102, 103, 109, 114, 117, 120, 133, 157, 170, 175, 187, 190, 192, 193, 198, 207, 226, 240, 241, 243, 261, 285, 300, 308, 332, 344, 351, 356, 360, 375, 384, 385, 390, 404, 411, 414, 415, 420, 424, 445, 450, 459, 462, 477, 480, 481

Offset: 1

Author

Altug Alkan, Jan 15 2016

Keywords

• nonn

Comments

See first comment in A004215.

Corresponding Catalan numbers are 16796, 1289904147324, 45950804324621742364, 150853479205085351660700, ...

It is obvious that minimum value of a(n) - a(n-1) is 1. Is there a maximum value of a(n) - a(n-1)?

Examples

			10 is a term because the 10th Catalan number is 16796 and there are no integer values of x, y and z for the equation 16796 = x^2 + y^2 + z^2.
		

Crossrefs

Cf. A000108, A004215, A000408.

Programs

PARI

isA004215(n) = { my(fouri, j) ; fouri=1 ; while( n >=7*fouri, if( n % fouri ==0, j= n/fouri -7 ; if( j % 8 ==0, return(1) ) ; ) ; fouri *= 4 ; ) ; return(0) ; } { for(n=1, 400, if(isA004215(n), print1(n, ", ") ; ) ; ) ; }
c(n) = binomial(2*n,n)/(n+1);
for(n=0, 1e3, if(isA004215(c(n)), print1(n, ", ")));