The On-Line Encyclopedia of Integer Sequences (OEIS)

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A145047

Primes p of the form 4k+1 for which s=10 is the least positive integer such that sp-(floor(sqrt(sp)))^2 is a square.
(history; published version)

#5 by Susanna Cuyler at Sun Jan 12 23:45:49 EST 2020

STATUS

proposed

approved

#4 by Jon E. Schoenfield at Sun Jan 12 20:23:33 EST 2020

STATUS

editing

proposed

#3 by Jon E. Schoenfield at Sun Jan 12 20:23:31 EST 2020

NAME

Primes p of the form 4k+1 for which s=10 is the least positive integer such that sp-(floor(sqrt(sp)))^2 is a full square.

COMMENTS

Conjecture. : The least positive integer s could can take values only from A008784 (see for s=1,2,5,10 sequences A145016, A145022, A145023 and this sequence).

EXAMPLE

a(1)=1237 since p=1237 is the least prime of the form 4k+1 for which sp-(floor(sqrt(sp)))^2 is not a full square for s=1,...,9, but 10p-(floor(sqrt(10p)))^2 is a full square (for p=1237 it is 49).

CROSSREFS

Cf. A145016 , A145017 , A145022 , A145023 , A008784.

STATUS

approved

editing

#2 by Russ Cox at Fri Mar 30 18:52:52 EDT 2012

AUTHOR

_Vladimir Shevelev (shevelev(AT)bgu.ac.il), _, Sep 30 2008, Oct 05 2008

Discussion

Fri Mar 30

18:52

OEIS Server: https://oeis.org/edit/global/261

#1 by N. J. A. Sloane at Fri Jan 09 03:00:00 EST 2009

NAME

Primes p of the form 4k+1 for which s=10 is the least positive integer such that sp-(floor(sqrt(sp)))^2 is a full square

DATA

1237, 1621, 1721, 1933, 1949, 1993, 2221, 2237, 2309, 2341, 2473, 2621, 2657, 2789, 2797, 2857, 2953, 3221, 3361, 3533, 3677, 3881, 3889, 3917, 4133, 4457, 4481, 4549, 4813, 4889, 4973, 5153, 5189, 5261, 5441, 5653, 5717, 5813, 6101, 6217, 6301, 6329

OFFSET

1,1

COMMENTS

Conjecture. The least positive integer s could take values only from A008784 (see for s=1,2,5,10 sequences A145016, A145022, A145023 and this sequence)

EXAMPLE

a(1)=1237 since p=1237 is the least prime of the form 4k+1 for which sp-(floor(sqrt(sp)))^2 is not a full square for s=1,...,9, but 10p-(floor(sqrt(10p)))^2 is a full square (for p=1237 it is 49)

CROSSREFS

A145016 A145017 A145022 A145023 A008784

KEYWORD

nonn

AUTHOR

Vladimir Shevelev (shevelev(AT)bgu.ac.il), Sep 30 2008, Oct 05 2008

STATUS

approved