A333443 - OEIS

%I #21 May 13 2020 07:04:46

%S 985,1585,1768,1780,2249,2329,2500,2929,3280,3649,3977,4264,4329,4705,

%T 4849,5017,5044,5065,5140,5161,5512,5617,5625,6340,6409,6697,7240,

%U 7684,7785,7956,7969,8020,8065,8320,8584,8905,9089,9265,9529,9553,9593,9700,9809

%N Numbers k such that both k and k+1 are sums of two positive squares in 2 or more ways.

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

%H Amiram Eldar, <a href="/A333443/b333443.txt">Table of n, a(n) for n = 1..10000</a>

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

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

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

%o (Python)

%o n=100

%o t=[]

%o prev=0

%o A333443=[]

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

%o     t.append(i*i)

%o for j in range(n**2):

%o     n=0

%o     for k in t[:j+1]:

%o         if j-k in t and k<=j-k:

%o             n=n+1

%o             if n>1:

%o                 if j-prev==1:

%o                     A333443.append(j-1)

%o                 prev=j

%Y Subsequence of A007692.

%Y Cf. A085323, A140612.

%K easy,nonn

%O 1,1

%A _Mateusz Winiarski_, Mar 21 2020