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 A245440 Primes p == 1 (mod 4) such that p - floor(sqrt(p))^2 and 2p - floor(sqrt(2p))^2 are not squares. 2
 353, 373, 449, 461, 521, 541, 593, 653, 673, 757, 769, 797, 821, 829, 941, 953, 1009, 1021, 1061, 1069, 1097, 1193, 1217, 1237, 1249, 1277, 1361, 1381, 1481, 1489, 1549, 1597, 1613, 1621, 1657, 1669, 1693, 1709, 1721, 1733, 1777, 1801, 1877, 1889, 1933, 1949 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Primes p of the form 4k+1 such that A053610(p) > 2 and A053610(2p) > 2. Note that p = a^2 + b^2 and 2p = (a+b)^2 + (a-b)^2 is the only way. So according to the definition the greedy algorithm cannot give such the sums of two squares. Interesting fact: a(n) = A145023(n) for all n < 25. Of course A145023 is a subsequence. Primes p == 1 (mod 4) such that A245474(p) > 2. LINKS Michael De Vlieger, Table of n, a(n) for n = 1..10461 (first 46 terms from Thomas Ordowski and Colin Barker) MATHEMATICA a245440Q[n_Integer] := If[   And[PrimeQ[n] == True, Mod[n, 4] == 1],   If[Or[IntegerQ[Sqrt[n - Floor[Sqrt[n]]^2]] == True,     IntegerQ[Sqrt[2*n - Floor[Sqrt[2*n]]^2]] == True], False, True],   False]; a245440[n_Integer] := Flatten[Position[Thread[a245440Q[Range[n]]],    True]]; a245440[300000]; (* Michael De Vlieger, Aug 05 2014 *) PROG (PARI) s=[]; forprime(p=2, 3000, if(p%4==1 && !issquare(p-floor(sqrt(p))^2) && !issquare(2*p-floor(sqrt(2*p))^2), s=concat(s, p))); s \\ Colin Barker, Jul 22 2014 (MAGMA) [p: p in PrimesUpTo(10000) | p mod 4 eq 1 and not IsSquare(p-Floor(Sqrt(p))^2) and not IsSquare(2*p-Floor(Sqrt(2*p))^2)]; // Vincenzo Librandi, Sep 19 2017 CROSSREFS Cf. A002144, A053610, A145016, A145023, A174806, A245474. Sequence in context: A279583 A156177 A104160 * A145023 A343714 A343715 Adjacent sequences:  A245437 A245438 A245439 * A245441 A245442 A245443 KEYWORD nonn AUTHOR Thomas Ordowski, Jul 22 2014 EXTENSIONS More terms from Colin Barker, Jul 22 2014 STATUS approved

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Last modified July 28 00:54 EDT 2021. Contains 346316 sequences. (Running on oeis4.)