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%I #10 May 07 2012 14:07:44
%S 0,1,2,5,11,27,29,46,76,167,133,348,521,1160,1364,3005,3571,9348,9349,
%T 20820,24476,64062,64079,123651,167761,439203,439204,1149850,1149851,
%U 3010348,3010349,7881195,7881196,20633238,20633239,54018520,54018521,141422323,141422324
%N Position of first occurrence of n in A182576.
%C Conjecture: for k > 12, a(2k) = a(2k-1) + 1.
%e First occurrence of 4 in A182576(n) has index 11, so a(4)=11.
%o (C)
%o #include <stdio.h> // GCC // ~880 secs
%o typedef unsigned long long U64;
%o U64 fibs[992], first[992], prpr=0, prev=1, current, n, sq;
%o long long ftop, fpos, terms;
%o int main(int argc, char **argv)
%o {
%o for (ftop=0; ftop<900; ++ftop) {
%o fibs[ftop] = current = prpr+prev;
%o if (current<prev) break;
%o prpr = prev, prev = current;
%o }
%o printf("%llu\n%llu\n%llu\n%llu\n",ftop,prev,prpr,(U64)-1-prev);
%o for (n=0; n < ((U64)1<<32); ++n) {
%o fpos=ftop-1, terms=0;
%o for (sq=n*n; sq>0 && fpos>=0; ++terms, sq-=fibs[fpos], --fpos) {
%o while (fibs[fpos]>sq && fpos>0) --fpos;
%o }
%o if (sq>0) { printf("Error!"); exit(1); }
%o if (first[terms]==0)
%o first[terms]=n, printf("%2llu %llu\n",terms,n);
%o }
%o for (n=0; n<ftop; ++n) printf("%llu, ", first[n]);
%o return 0;
%o }
%Y Cf. A182576.
%K nonn
%O 0,3
%A _Alex Ratushnyak_, May 05 2012
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