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

Author

Antti Karttunen, Oct 10 2015

Keywords

• nonn

Comments

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

Examples

			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.
		

Links

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

Crossrefs

Cf. A000196, A002182, A263096, A263098.

Programs

Scheme

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

Formula

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