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 A281229 Smallest number k of the form x^2 + y^2 with 0 <= x <= y such that gcd(x, y) = 1, x + y = n, and k has no other decompositions into a sum of two squares. 1
 1, 2, 5, 10, 13, 26, 29, 34, 41, 58, 61, 74, 89, 106, 113, 146, 149, 194, 181, 202, 233, 274, 269, 386, 313, 346, 389, 394, 421, 458, 521, 514, 557, 586, 613, 698, 709, 794, 761, 802, 853, 914, 929, 1018, 1013, 1186, 1109, 1154, 1201, 1282, 1301, 1354, 1409 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Conjecture: for each n there exists such a number k. Note: a(2m+1) > 1 is a prime p and a(2m) > 2 is a double prime 2q, where p and q are primes == 1 (mod 4). For odd n > 1, a(n) is the smallest prime of the form x^2 + (n - x)^2. For even n > 2, a(n) is the smallest double prime of the above form. LINKS Robert Israel, Table of n, a(n) for n = 1..10000 FORMULA For m > 0, a(2m+1) = A159351(m). For m > 1, a(2m) = 2 * A068486(m). MAPLE f:= proc(n) local k, v;   for k from ceil(n/2) to n do     v:= k^2+(n-k)^2;     if n::odd then if isprime(v) then return v fi     elif isprime(v/2) then return v     fi   od;   FAIL end proc: f(1):=1: f(2):= 2: map(f, [\$1..100]); # Robert Israel, Dec 30 2020 PROG (PARI) isok(k, n) = {nba = 0; nbb = 0; for (x=0, k, if (issquare(x) && issquare(k-x), if (x <= k - x, nba++; if (nba > 1, return (0)); rx = sqrtint(x); ry = sqrtint(k-x); if ((gcd(rx, ry)==1) && (rx+ry == n), nbb++; ); ); ); ); if (nbb, return (k), return(0)); } a(n) = {k = 1; while (! (s = isok(k, n)), k++; ); s; } \\ Michel Marcus, Jan 20 2017 CROSSREFS Cf. A002144, A068486, A159351. Sequence in context: A064233 A051952 A103188 * A185647 A064392 A328700 Adjacent sequences:  A281226 A281227 A281228 * A281230 A281231 A281232 KEYWORD nonn AUTHOR Thomas Ordowski, Jan 18 2017 EXTENSIONS More terms from Altug Alkan, Jan 18 2017 More terms from Jon E. Schoenfield, Jan 18 2017 STATUS approved

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Last modified July 29 09:41 EDT 2021. Contains 346344 sequences. (Running on oeis4.)