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%I #16 Nov 13 2016 17:06:48
%S 10,24,37,43,46,48,49,51,69,87,96,97,102,103,109,114,117,120,133,157,
%T 170,175,187,190,192,193,198,207,226,240,241,243,261,285,300,308,332,
%U 344,351,356,360,375,384,385,390,404,411,414,415,420,424,445,450,459,462,477,480,481
%N Indices of Catalan numbers that are not of the form x^2 + y^2 + z^2 where x, y and z are integers.
%C See first comment in A004215.
%C Corresponding Catalan numbers are 16796, 1289904147324, 45950804324621742364, 150853479205085351660700, ...
%C 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)?
%e 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.
%o (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, ", ") ; ) ; ) ; }
%o c(n) = binomial(2*n,n)/(n+1);
%o for(n=0, 1e3, if(isA004215(c(n)), print1(n, ", ")));
%Y Cf. A000108, A004215, A000408.
%K nonn
%O 1,1
%A _Altug Alkan_, Jan 15 2016
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