The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A025320 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A025320

Numbers that are the sum of 2 distinct nonzero squares in 10 or more ways.
(history; published version)

#30 by N. J. A. Sloane at Sat Feb 27 10:01:33 EST 2016

STATUS

reviewed

approved

#29 by Vaclav Kotesovec at Sat Feb 27 09:55:50 EST 2016

STATUS

proposed

reviewed

#28 by Chai Wah Wu at Sat Feb 27 09:52:32 EST 2016

STATUS

editing

proposed

#27 by Chai Wah Wu at Sat Feb 27 09:51:51 EST 2016

COMMENTS

Numbers in A025301 but not in A025320 are exactly those numbers of the form 2*p_1^(2*a_1)*p_2^(2*a_2)*...*p_m^(2*a_m)*q^18 where p_i are primes of the form 4k+3 and q is a prime of the form 4k+1. Thus 2*5^18 is the smallest term inA025301 in A025301 that is not in A025320. - Chai Wah Wu, Feb 27 2016

Numbers in A025301 but not in A025320 are exactly those numbers of the form 2*p_1^(2*a_1)*p_2^(2*a_2)*...*p_m^(2*a_m)*q^18 where p_i are primes of the form 4k+3 and q is a prime of the form 4k+1. Thus 2*5^18 is the smallest term inA025301 that is not in A025320. - Chai Wah Wu, Feb 27 2016

#26 by Chai Wah Wu at Sat Feb 27 09:45:51 EST 2016

COMMENTS

Numbers in A025301 but not in A025320 are exactly those numbers of the form 2*p_1^(2*a_1)*p_2^(2*a_2)*...*p_m^(2*a_m)*q^18 where p_i are primes of the form 4k+3 and q is a prime of the form 4k+1. Thus 2*5^18 is the smallest term inA025301 that is not in A025320. - Chai Wah Wu, Feb 27 2016

#25 by Chai Wah Wu at Sat Feb 27 09:40:46 EST 2016

COMMENTS

Numbers in A025301 but not in A025320 are exactly those numbers of the form 2*p_1^(2*a_1)*p_2^(2*a_2)*...*p_m^(2*a_m)*q^18 where p_i are primes of the form 4k+3 and q is a prime of the form 4k+1. Thus 2*5^18 is the smallest term inA025301 that is not in A025320. - Chai Wah Wu, Feb 27 2016

STATUS

proposed

editing

#24 by Vaclav Kotesovec at Sat Feb 27 09:26:33 EST 2016

STATUS

editing

proposed

#23 by Vaclav Kotesovec at Sat Feb 27 09:16:40 EST 2016

COMMENTS

Subsequence of A025301. But sequences A025320 and A025301 are different. 2*5^18 = 7629394531250 = 182125^2 + 2756125^2 = 390625^2 + 2734375^2 = 596875^2 + 2696875^2 = 799687^2 + 2643841^2 = 946555^2 + 2594885^2 = 1140625^2 + 2515625^2 = 1328125^2 + 2421875^2 = 1507975^2 + 2314175^2 = 1799375^2 + 2095625^2 = 1953125^2 + 1953125^2 (not distinct squares) is not in A025320. - Vaclav Kotesovec, Feb 27 2016

#22 by Vaclav Kotesovec at Sat Feb 27 09:03:02 EST 2016

COMMENTS

Appears to be the same sequence as A025301. - Chai Wah Wu, Feb 26 2016

STATUS

reviewed

editing

Discussion

Sat Feb 27

09:04

Vaclav Kotesovec: Counterexample is 2*5^18 = 7629394531250 which is in A025301, but not in A025320

#21 by Joerg Arndt at Sat Feb 27 08:17:05 EST 2016

STATUS

proposed

reviewed