login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A058056 a(n) = p is the smallest prime such that p = n + h(n)^2 and p is the first prime following h(n)^2. The smallest immediate post-square primes with distance n = p - h(n)^2. 2

%I

%S 2,11,67,29,149,127,331,2609,6733,2411,54767,541,1777,5639,7411,53377,

%T 30293,11467,82963,3989,6421,4783,10427,105649,27581,585251,16411,

%U 20477,675713,528559,76207,356441,51109,697259,492839,212557,64553,480287,350503,635249

%N a(n) = p is the smallest prime such that p = n + h(n)^2 and p is the first prime following h(n)^2. The smallest immediate post-square primes with distance n = p - h(n)^2.

%C The primes generated by the numbers in A058055.

%H T. D. Noe, <a href="/A058056/b058056.txt">Table of n, a(n) for n = 1..400</a>

%e For n=5, a(5) = 149 = 5+144 = 5+12^2; although 41 = 5+36 = 5+k^2 but between 41 and 36 further prime occurs 37 while no more primes are between 144 and 149. n=7 a(7) = 331 = 324+7 = 18*18+7 and 331 = nextprime(324); numerous smaller primes (like {7, 11, 23, 43, 71, 107, 151, 263} = 7 + {0, 4, 16, 36, 64, 100, 144, 256}) have q = 7+k^2 form so that q is not the nextprime(7+k^2), 324 is the smallest square of this kind.

%t nn = 100; t = Table[0, {nn}]; found = 0; m = 0; While[found < nn, m++; k = NextPrime[m^2] - m^2; If[k <= nn && t[[k]] == 0, t[[k]] = m^2 + k; found++]]; t (* _T. D. Noe_, Aug 12 2012 *)

%K nonn

%O 1,1

%A _Labos Elemer_, Nov 20 2000

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.

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 10 16:24 EDT 2022. Contains 356039 sequences. (Running on oeis4.)