A333443 Numbers k such that both k and k+1 are sums of two positive squares in 2 or more ways.
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
Examples
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.
Links
- Amiram Eldar, Table of n, a(n) for n = 1..10000
Programs
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Mathematica
ok[n_] := Length@ IntegerPartitions[n, {2}, Range[Sqrt@ n]^2] >= 2; Select[ Range@ 10000, ok[#] && ok[#+1] &] (* Giovanni Resta, Mar 24 2020 *) -
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
Comments