The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A260815 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A260815

a(2) = 3; for n >= 3, a(n) = a(n-1) + gcd(n, a(n-1))^2.
(history; published version)

#20 by N. J. A. Sloane at Sun Aug 02 17:38:52 EDT 2015

COMMENTS

The first differences of a(n) are all squares.

STATUS

proposed

editing

Discussion

Sun Aug 02

17:39

N. J. A. Sloane: restored the comment

#19 by Arkadiusz Wesolowski at Sun Aug 02 08:54:47 EDT 2015

STATUS

editing

proposed

#18 by Arkadiusz Wesolowski at Sun Aug 02 08:54:41 EDT 2015

COMMENTS

The first differences of a(n) are all squares.

#17 by Alonso del Arte at Sat Aug 01 22:13:59 EDT 2015

EXAMPLE

a(3) = 3 + gcd(3, 3)^2 = 3 + 9 = 12.

a(4) = 12 + gcd(4, 12)^2 = 12 + 16 = 28.

a(5) = 28 + gcd(5, 28)^2 = 28 + 1 = 29.

STATUS

proposed

editing

Discussion

Sat Aug 01

22:34

Alonso del Arte: Is there something more meaningful or interesting to say about the first differences? If not, I suggest deleting that line.

#16 by Arkadiusz Wesolowski at Sat Aug 01 06:23:40 EDT 2015

STATUS

editing

proposed

#15 by Arkadiusz Wesolowski at Sat Aug 01 06:23:14 EDT 2015

PROG

(MAGMA) I:=[0, 3]; Remove([n le 2 select I[n] else Self(n-1)+Gcd(n, Self(n-1))^2: n in [1..52]], 1);

#14 by Arkadiusz Wesolowski at Sat Aug 01 06:10:02 EDT 2015

COMMENTS

It appears that the The first differences of a(n) are all squares.

#13 by Joerg Arndt at Sat Aug 01 06:05:03 EDT 2015

STATUS

proposed

editing

#12 by Arkadiusz Wesolowski at Fri Jul 31 14:43:25 EDT 2015

STATUS

editing

proposed

Discussion

Sat Aug 01

06:04

Joerg Arndt: "It appears ..."?  That's by definition!

#11 by Arkadiusz Wesolowski at Fri Jul 31 14:42:07 EDT 2015

NAME

a(1) = 2, a(2) = 3; for n > 2, = 3, a(n) = a(n-1) + gcd(n, a(n-1))^2.

DATA

2, 3, 12, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 575, 576, 577, 578, 579, 580, 1421, 1422, 1423, 1424, 1425, 1426, 1427, 1428, 1429, 1430, 1599, 1600, 1601, 1602, 1603, 1604, 1605, 1606, 1607, 1608, 1609, 1610, 1611, 1612

OFFSET

1,2,1

PROG

(MAGMA) I:=[2, 3]; [n le 2 select I[n] else Self(n-1)+Gcd(n, Self(n-1))^2: n in [1..51]];