A263097 First differences of A263096.

0, 1, 0, 1, 1, 2, 0, 1, 3, 3, 2, 3, 8, 2, 7, 5, 10, 20, 16, 14, 22, 19, 17, 8, 46, 12, 11, 53, 44, 75, 63, 56, 50, 130, 38, 71, 33, 191, 161, 270, 227, 201, 181, 467, 138, 256, 347, 509, 362, 491, 1045, 368, 513, 1251, 747, 1927, 568, 1057, 1431, 2097, 1494, 2025, 4308, 2946, 687, 6093, 4167, 8399, 1189, 1287, 4605, 6239, 9141, 6513, 8822, 18782, 15834, 26561, 22392, 37564, 16401, 32375, 17317, 12602

Offset

1,6

Comments

a(n) = number of perfect squares in range [A002182(n)+1 .. A002182(n+1)].

Links

Antti Karttunen, Table of n, a(n) for n = 1..999 (based on the b-file of A002182 provided by T. D. Noe.)

Formula

a(n) = A263096(n+1) - A263096(n).

Example

A002182 begins as 1, 2, 4, 6, 12, 24, 36, 48, 60, 120, ...
In range [2,2] there are no squares, so a(1) = 0.
In range [3,4] there is one square, so a(2) = 1.
In range [5,6] there are no squares, so a(3) = 0.
In range [7,12] there is one square, so a(4) = 1.
In range [13,24] there is one square, so a(5) = 1.
In range [25,36] there are two squares, so a(6) = 2.
In range [37,48] there are no squares, so a(7) = 0.
In range [49,60] there is one square, so a(8) = 1.
In range [61,120] there are three squares (64, 81, 100), thus a(9) = 3.

Prog

(Scheme) (define (A263097 n) (- (A263096 (+ n 1)) (A263096 n)))

Crossrefs

Cf. A000196, A002182, A263096, A263098.

Sequence in context: A124031 A368514 A289229 * A286011 A241954 A307047

Adjacent sequences: A263094 A263095 A263096 * A263098 A263099 A263100

Keyword

nonn

Author

Antti Karttunen, Oct 10 2015

Status

approved