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A333443 Numbers k such that both k and k+1 are sums of two positive squares in 2 or more ways. 1
985, 1585, 1768, 1780, 2249, 2329, 2500, 2929, 3280, 3649, 3977, 4264, 4329, 4705, 4849, 5017, 5044, 5065, 5140, 5161, 5512, 5617, 5625, 6340, 6409, 6697, 7240, 7684, 7785, 7956, 7969, 8020, 8065, 8320, 8584, 8905, 9089, 9265, 9529, 9553, 9593, 9700, 9809 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Numbers k such that both k and k+1 belong to A007692.

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000

EXAMPLE

985 is a term since 12^2 + 29^2 = 16^2 + 27^2 = 985 and 5^2 + 31^2 = 19^2 + 25^2 = 986.

625 is not a term because 626 cannot be written as the sum of two positive squares in more than one way.

MATHEMATICA

ok[n_] := Length@ IntegerPartitions[n, {2}, Range[Sqrt@ n]^2] >= 2; Select[ Range@ 10000, ok[#] && ok[#+1] &] (* Giovanni Resta, Mar 24 2020 *)

PROG

(Python)

n=100

t=[]

prev=0

A333443=[]

for i in range(1, n+1):

    t.append(i*i)

for j in range(n**2):

    n=0

    for k in t[:j+1]:

        if j-k in t and k<=j-k:

            n=n+1

            if n>1:

                if j-prev==1:

                    A333443.append(j-1)

                prev=j

CROSSREFS

Subsequence of A007692.

Cf. A085323, A140612.

Sequence in context: A288840 A289417 A131640 * A183718 A163025 A069299

Adjacent sequences:  A333440 A333441 A333442 * A333444 A333445 A333446

KEYWORD

easy,nonn

AUTHOR

Mateusz Winiarski, Mar 21 2020

STATUS

approved

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Last modified October 6 07:09 EDT 2022. Contains 357262 sequences. (Running on oeis4.)