

A263097


First differences of A263096.


3



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



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 bfile 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: A297477 A124031 A289229 * A286011 A241954 A307047
Adjacent sequences: A263094 A263095 A263096 * A263098 A263099 A263100


KEYWORD

nonn


AUTHOR

Antti Karttunen, Oct 10 2015


STATUS

approved



