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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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified October 6 07:09 EDT 2022. Contains 357262 sequences. (Running on oeis4.)