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

Author

Mateusz Winiarski, Mar 21 2020

Keywords

• easy
• nonn

Comments

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

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

Crossrefs

Subsequence of A007692.

Cf. A085323, A140612.

Programs

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