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, 11, 67, 29, 149, 127, 331, 2609, 6733, 2411, 54767, 541, 1777, 5639, 7411, 53377, 30293, 11467, 82963, 3989, 6421, 4783, 10427, 105649, 27581, 585251, 16411, 20477, 675713, 528559, 76207, 356441, 51109, 697259, 492839, 212557, 64553, 480287, 350503, 635249

Offset

1,1

Comments

The primes generated by the numbers in A058055.

Links

T. D. Noe, Table of n, a(n) for n = 1..400

Example

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.

Mathematica

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 *)

Crossrefs

Sequence in context: A216585 A245277 A138792 * A266579 A063768 A042245

Adjacent sequences: A058053 A058054 A058055 * A058057 A058058 A058059

Keyword

nonn

Author

Labos Elemer, Nov 20 2000

Status

approved