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

1,1

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