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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
OFFSET
1,1
COMMENTS
Numbers k such that both k and k+1 belong to A007692.
LINKS
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
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.
Sequence in context: A288840 A289417 A131640 * A183718 A163025 A069299
KEYWORD
easy,nonn
AUTHOR
Mateusz Winiarski, Mar 21 2020
STATUS
approved