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

1,1

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)?

Links

Table of n, a(n) for n=1..58.

Example

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.

Prog

(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, ", ")));

Crossrefs

Cf. A000108, A004215, A000408.

Sequence in context: A076675 A063925 A101156 * A162817 A103573 A067728

Adjacent sequences: A267428 A267429 A267430 * A267432 A267433 A267434

Keyword

nonn

Author

Altug Alkan, Jan 15 2016

Status

approved