OFFSET
1,3
COMMENTS
The starting point ((n+1)^2)-1 of the iteration is included if it is odd, but the ending point (n^2)-1 is never included in the count.
a(n) = number of odd numbers on row n of A276574, after the initial zero-row.
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..10000
A. Karttunen, Ratio a(n)/A277890(n) drawn with OEIS Plot 2 tool
EXAMPLE
For n=6, we start iterating from k = ((6+1)^2)-1 = 48, with k -> k - A002828(k), to obtain 48 -> 45 -> 43 -> 40 -> 38 before reaching 35 (which is 6^2 - 1, an ending point and thus not included in the count), and the only odd numbers before that were 45 and 43, thus a(6) = 2.
PROG
(PARI)
istwo(n:int)=my(f); if(n<3, return(n>=0); ); f=factor(n>>valuation(n, 2)); for(i=1, #f[, 1], if(bitand(f[i, 2], 1)==1&&bitand(f[i, 1], 3)==3, return(0))); 1
isthree(n:int)=my(tmp=valuation(n, 2)); bitand(tmp, 1)||bitand(n>>tmp, 7)!=7
A002828(n)=if(issquare(n), !!n, if(istwo(n), 2, 4-isthree(n))) \\ From _Charles R Greathouse_ IV, Jul 19 2011
A277891(n) = { my(orgk = ((n+1)^2)-1); my(k = orgk, s = 0); while(((k == orgk) || !issquare(1+k)), s = s + (k%2); k = k - A002828(k)); s; };
for(n=1, 10000, write("b277891.txt", n, " ", A277891(n)));
(Scheme)
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Nov 08 2016
STATUS
approved