The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A278491 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A278491

After a(0)=0, numbers n such that (A002828(1+n) = 1) and (A002828(4+n) = 4).
(history; published version)

#14 by N. J. A. Sloane at Sun Nov 27 22:06:36 EST 2016

STATUS

proposed

approved

#13 by Antti Karttunen at Sat Nov 26 16:35:33 EST 2016

STATUS

editing

proposed

#12 by Antti Karttunen at Sat Nov 26 16:34:25 EST 2016

PROG

\\ (For a more intelligent way to generate the terms, check Altug Alkan's PARI-code for A273324).

#11 by Antti Karttunen at Sat Nov 26 16:20:26 EST 2016

FORMULA

For a(0) = 0, and for n >= 1, a(n) = A273324(n)^2 - 1.

#10 by Antti Karttunen at Sat Nov 26 16:19:13 EST 2016

FORMULA

For n >= 1, a(n) = (A273324(n)^2 - 1.

#9 by Antti Karttunen at Sat Nov 26 16:18:39 EST 2016

NAME

After a(0)=0, numbers n such that (A002828(1+n) = 1), (A002828(2+n) = 2), (A002828(3+n) = 3) and (A002828(4+n) = 4).

COMMENTS

In the terms of tree defined by edge relation A255131(child) = parent, ("the least squares beanstalk"), these numbers are nodes with four children (maximum possible), which also implies that they must be all included in the infinite trunk of that tree, A276573.

Indexing starts from zero, because a(0)=0 is a special case in this sequence, as it is only number which is its own child in the least squares beanstalk tree.

The definition implies that after 0 these are also all numbers n such that (A002828(1+n) = 1), (A002828(2+n) = 2), (A002828(3+n) = 3) and (A002828(4+n) = 4).

In the terms of tree defined by edge relation A255131(child) = parent, ("the least squares beanstalk"), these numbers are the nodes with four children (maximum possible).

Either of the above facts implies that this is a subsequence of A276573.

Indexing starts from zero, because a(0)=0 is a special case in this sequence, as it is only number which is its own child in the least squares beanstalk tree.

#8 by Antti Karttunen at Sat Nov 26 16:15:14 EST 2016

PROG

isA278491(n) = (!n || ((A002828(1+n) == 1) && (A002828(2+n) == 2) && (A002828(3+n) == 3) && (A002828(4+n) == 4)));

#7 by Antti Karttunen at Sat Nov 26 15:56:40 EST 2016

LINKS

Antti Karttunen, <a href="/A278491/b278491.txt">Table of n, a(n) for n = 0..10000</a>

Discussion

Sat Nov 26

16:14

Antti Karttunen: Just a slightly less naive:

#6 by Antti Karttunen at Sat Nov 26 15:35:53 EST 2016

FORMULA

For n >= 1, a(n) = (A273324(n)^2 - 1.

CROSSREFS

Cf. A002828, A273324, A278216.

Discussion

Sat Nov 26

15:55

Antti Karttunen: My PARI-program is ultra-naive, now that I saw Altug Alkan's A273324.

#5 by Antti Karttunen at Sat Nov 26 15:29:33 EST 2016

COMMENTS

Because A002828 obtains value 1 only at squares, every term must be one less than a square.

CROSSREFS

Subsequence of A005563, A276573 and of A278489.