The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A069003 Smallest integer d such that n^2 + d^2 is a prime number. 19
 1, 1, 2, 1, 2, 1, 2, 3, 4, 1, 4, 7, 2, 1, 2, 1, 2, 5, 6, 1, 4, 5, 8, 1, 4, 1, 2, 5, 4, 11, 4, 3, 2, 5, 2, 1, 2, 3, 10, 1, 4, 5, 8, 9, 2, 5, 2, 13, 4, 7, 4, 3, 10, 1, 4, 1, 2, 3, 6, 13, 10, 3, 32, 9, 2, 1, 2, 5, 10, 3, 6, 5, 2, 1, 4, 5, 10, 7, 4, 7, 4, 3, 18, 1, 2, 9, 2, 3, 4, 1, 4, 7, 8, 1, 2, 5, 2, 3, 4, 3 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS With i being the imaginary unit, n + di is the smallest Gaussian prime with real part n and a positive imaginary part. Likewise for n - di. See A002145 for Gaussian primes with imaginary part 0. - Alonso del Arte, Feb 07 2011 Conjecture: a(n) does not exceed 4*sqrt(n+1) for any positive integer n. - Zhi-Wei Sun, Apr 15 2013 Conjecture holds for the first 15*10^6 terms. - Joerg Arndt, Aug 19 2014 Infinitely many d exist such that n^2 + d^2 is prime, under Schinzel's Hypothesis H; see Sierpinski (1988), p. 221. - Jonathan Sondow, Nov 09 2015 REFERENCES W. Sierpinski, Elementary Theory of Numbers, 2nd English edition, revised and enlarged by A. Schinzel, Elsevier, 1988. LINKS T. D. Noe and Zhi-Wei Sun (with the first 1000 terms from Noe), Table of n, a(n) for n = 1..10000 Eric Weisstein's World of Mathematics, Gaussian Prime Wikipedia, Schinzel's Hypothesis H EXAMPLE a(5)=2 because 2 is the smallest integer d such that 5^2+d^2 is a prime number. MAPLE f:= proc(n) local d;      for d from 1+(n mod 2) by 2 do        if isprime(n^2+d^2) then return d fi      od end proc: f(1):= 1: map(f, [\$1..1000]); # Robert Israel, Jul 06 2015 MATHEMATICA imP4P[n_] := Module[{k = 1}, While[Not[PrimeQ[n^2 + k^2]], k++]; k]; Table[imP4P[n], {n, 50}] (* Alonso del Arte, Feb 07 2011 *) PROG (PARI) a(n)=my(k); while(!isprime(n^2+k++^2), ); k \\ Charles R Greathouse IV, Mar 20 2013 CROSSREFS Cf. A068486 (lists the prime numbers n^2 + d^2). Cf. A185636, A204065. Cf. A239388, A239389 (record values). Cf. A053000. Sequence in context: A177803 A274080 A074641 * A087855 A083409 A317586 Adjacent sequences:  A069000 A069001 A069002 * A069004 A069005 A069006 KEYWORD easy,nonn AUTHOR T. D. Noe, Apr 02 2002 STATUS approved

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

Last modified June 2 11:35 EDT 2020. Contains 334771 sequences. (Running on oeis4.)