A277890 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

A277890

Number of even numbers encountered before (n^2)-1 is reached when starting from k = ((n+1)^2)-1 and iterating map k -> k - A002828(k).

7

0, 2, 0, 3, 2, 3, 1, 5, 3, 4, 4, 6, 3, 5, 3, 7, 8, 8, 6, 8, 9, 10, 6, 8, 10, 10, 7, 11, 10, 13, 11, 12, 12, 14, 10, 13, 12, 13, 14, 15, 13, 15, 15, 18, 18, 16, 15, 17, 21, 18, 18, 18, 19, 20, 16, 21, 20, 20, 22, 20, 23, 20, 22, 23, 21, 23, 23, 27, 25, 24, 22, 28, 22, 27, 24, 26, 25, 25, 29, 29, 28, 26, 30, 31, 28, 28, 31, 30, 32, 33, 27, 32, 34, 34, 30, 33, 33

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

The starting point ((n+1)^2)-1 of the iteration is included if it is even, but the ending point (n^2)-1 is never included in the count.

a(n) = number of even numbers on row n of A276574, after the initial zero-row.

See also comments in A277891.

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..10000

FORMULA

a(n) + A277891(n) = A260734(n).

For n >= 2, a(n) >= A277486(n).

a(n) >= A277488(n).

EXAMPLE

For n=6, we start iterating from k = ((6+1)^2)-1 = 48, and then 48 - A002828(48) = 45, 45 - A002828(45) = 43, 43 - A002828(43) = 40, 40 - A002828(40) = 38, and 38 - A002828(38) = 35 (which is 6^2 - 1), and three of these numbers are even, thus a(6) = 3.

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

A277890(n) = { my(orgk = ((n+1)^2)-1); my(k = orgk, s = 0); while(((k == orgk) || !issquare(1+k)), s = s + (1-(k%2)); k = k - A002828(k)); s; };

for(n=1, 10000, write("b277890.txt", n, " ", A277890(n)));

(Scheme)

(define (A277890 n) (let ((org_k (- (A000290 (+ 1 n)) 1))) (let loop ((k org_k) (s 0)) (if (and (< k org_k) (= 1 (A010052 (+ 1 k)))) s (loop (- k (A002828 k)) (+ s (- 1 (A000035 k))))))))

CROSSREFS

Cf. A000035, A000290, A002828, A010052, A260734, A276573, A276574, A277486, A277488, A277889, A277891.

Sequence in context: A323248 A324397 A132623 * A243403 A051613 A173291

Adjacent sequences: A277887 A277888 A277889 * A277891 A277892 A277893

KEYWORD

nonn

AUTHOR

Antti Karttunen, Nov 08 2016

STATUS

approved