The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A133388 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A133388

Largest integer m such that n-m^2 is a square, or 0 if no such m exists.
(history; published version)

#38 by Joerg Arndt at Tue Sep 24 02:11:56 EDT 2024

STATUS

reviewed

approved

#37 by Michel Marcus at Tue Sep 24 01:16:06 EDT 2024

STATUS

proposed

reviewed

#36 by Jason Yuen at Mon Sep 23 22:38:34 EDT 2024

STATUS

editing

proposed

#35 by Jason Yuen at Mon Sep 23 22:38:30 EDT 2024

MATHEMATICA

Table[a[n], {n, 1, 100}] (* Jean-François Alcover, May 18 2018, after Alois P. Heinz *) *)

STATUS

approved

editing

#34 by Alois P. Heinz at Thu Sep 08 10:41:50 EDT 2022

STATUS

reviewed

approved

#33 by Michel Marcus at Thu Sep 08 10:39:54 EDT 2022

STATUS

proposed

reviewed

#32 by Chai Wah Wu at Thu Sep 08 10:36:28 EDT 2022

STATUS

editing

proposed

#31 by Chai Wah Wu at Thu Sep 08 10:36:19 EDT 2022

PROG

(Python)

from sympy.solvers.diophantine.diophantine import diop_DN

def A133388(n): return max((a for a, b in diop_DN(-1, n)), default=0) # Chai Wah Wu, Sep 08 2022

STATUS

approved

editing

#30 by M. F. Hasler at Mon Jun 20 09:16:17 EDT 2022

STATUS

editing

approved

#29 by M. F. Hasler at Mon Jun 20 09:14:11 EDT 2022

PROG

(PARI) sum2sqr(n)={ if(n>1, my(L=List(), f, p=1); for(i=1, matsize(f=factor(n))[1], if(f[i, 1]%4==1, listput(L, [qfbsolve(Qfb(1, 0, 1), f[i, 1])*[1, I]~, f[i, 2]] ), /*elseif*/ f[i, 1]==2, p = (1+I)^f[i, 2], /*elseif*/ bittest(f[i, 2], 0), return([]), /*else*/ p *= f[i, 1]^(f[i, 2]\2))); L=apply(s->vector(s[2]+1, j, s[1]^(s[2]+1-j)*conj(s[1])^(j-1)), L); my(S=List()); forvec(T=vector(#L, i, [1, #L[i]]), listput(S, prod( j=1, #T, L[j][T[j]] ))); Set(apply(f->vecsort(abs([real(f), imag(f)])), Set(S)*p)), if(n<0, [], [[0, n]]))} \\ updated by M. F. Hasler, May 12 2018 \\ NOTE: for . (If PARI version >= 2.12.0, x returns an error, append [1] to qfbsolve(...) above which now returns a vector of results! . - M. F. Hasler, Dec 12 2019)

STATUS

approved

editing

Discussion

Mon Jun 20

09:16

M. F. Hasler: Comment seems no more relevant - appears to work correctly as is, in PARI 2.13.1.