The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A214750 Least m > 0 such that n - m divides n^2 + m^2. 3
 1, 1, 2, 3, 2, 5, 4, 3, 2, 9, 3, 11, 6, 5, 8, 15, 6, 17, 4, 3, 11, 21, 6, 15, 13, 9, 12, 27, 5, 29, 16, 11, 17, 10, 4, 35, 19, 13, 8, 39, 6, 41, 12, 15, 23, 45, 12, 35, 10, 17, 20, 51, 18, 5, 7, 19, 29, 57, 10, 59, 31, 9, 32, 15, 22, 65, 34, 23, 14, 69, 8, 71, 37, 25, 38 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,3 COMMENTS It appears that this is the sequence of k's for A110357. - Michel Marcus, Aug 16 2019 If n-m = s, then n = s+m and n-m | n^2+m^2 is equivalent to s | (s^2 + 2*s*m + 2*m^2). So n-m | n^2+m^2 is equivalent to n-m | 2*m^2. If n-k = s, then n = s+k and n-k | n*(n+k) is equivalent to s | (s^2 + 3*s*k + 2*k^2). So n-k | n*(n+k) is equivalent to n-k | 2*k^2. Therefore n-m | n^2+m^2 is equivalent to n-k | n*(n+k) and the k's from A110357 and the m's from this sequence are the same. - Bob Andriesse, Dec 26 2022 Let n-m = s; then m = n-s and n-m | n^2 + m^2 is equivalent to s | n^2 + (n-s)^2 or s | 2*n^2. If n is an odd prime, s must be 2. So if n is an odd prime, a(n) = m = n-2. Examples: a(7) = 5, a(11) = 9. - Bob Andriesse, Jul 13 2023 LINKS Clark Kimberling, Table of n, a(n) for n = 2..1000 FORMULA a(n) = H(n, A110357(n)) - n where H is the harmonic mean. - Bob Andriesse, Jan 03 2023 EXAMPLE Write x#y if x|y is false; then 7#65, 6#68, 5#73, 4|80, so a(8) = 4. For n = 11, A110357(11) = 110 and a(11) = H(11, 110) - 11 = 20 - 11 = 9. - Bob Andriesse, Jan 03 2023 MATHEMATICA Table[m = 1; While[! Divisible[n^2+m^2, n-m], m++]; m, {n, 2, 100}] PROG (PARI) a(n) = my(m=1); while(denominator((n^2+m^2)/(n-m)) != 1, m++); m; \\ Michel Marcus, Aug 16 2019 (Python) from sympy.abc import x, y from sympy.solvers.diophantine.diophantine import diop_quadratic def A214750(n): return min(int(x) for x, y in diop_quadratic(n*(n-y)+x*(y+x)) if x>0) # Chai Wah Wu, Oct 06 2023 CROSSREFS Cf. A110357, A214749. Sequence in context: A263216 A141663 A011153 * A317585 A132226 A197702 Adjacent sequences: A214747 A214748 A214749 * A214751 A214752 A214753 KEYWORD nonn,easy AUTHOR Clark Kimberling, Jul 29 2012 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified June 14 04:14 EDT 2024. Contains 373393 sequences. (Running on oeis4.)