The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A305292

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A305292

Numbers k such that k-1 is a square and k+1 is a triangular number.
(history; published version)

#18 by Alois P. Heinz at Thu Jun 14 16:45:02 EDT 2018

STATUS

reviewed

approved

#17 by Michel Marcus at Thu Jun 14 12:16:56 EDT 2018

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proposed

reviewed

#16 by Colin Barker at Thu Jun 14 11:41:31 EDT 2018

STATUS

editing

proposed

#15 by Colin Barker at Thu Jun 14 11:41:04 EDT 2018

LINKS

Colin Barker, <a href="/A305292/b305292.txt">Table of n, a(n) for n = 1..1000</a>

PROG

(PARI) Vec(x*(2 + 3*x - 8*x^2 + 3*x^3 + 2*x^4)/((1 - x)*(1 - 6*x + x^2)*(1 + 6*x + x^2)) + O(x^30)) \\ Colin Barker, Jun 14 2018

STATUS

approved

editing

#14 by Giovanni Resta at Thu Jun 14 11:12:59 EDT 2018

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reviewed

approved

#13 by Joerg Arndt at Thu Jun 14 10:54:19 EDT 2018

STATUS

proposed

reviewed

#12 by Bruno Berselli at Thu Jun 14 09:32:20 EDT 2018

STATUS

editing

proposed

#11 by Bruno Berselli at Thu Jun 14 09:28:47 EDT 2018

NAME

Numbers which are between k such that k-1 is a square and k+1 is a triangular number.

COMMENTS

a(n)-1 is a square and a(n)+1 is a triangular number. It is easy to prove that there are no numbers k such that k-1 is a triangular number and k+1 is a square.

#10 by Bruno Berselli at Thu Jun 14 09:06:43 EDT 2018

COMMENTS

a(n)-1 is a square and a(n)+1 is a triangular number. It is easy to prove that there are no numbers k such that k-1 is a triangular number and k+1 is a square.

#9 by Bruno Berselli at Tue Jun 12 08:56:47 EDT 2018

FORMULA

a(n) = A214838(n) - 1.

a(n) = A077241(n-1)^2 + 1.

CROSSREFS

Cf. A000045, A000290, A077241, A214838.