A090117 a(n) = x^2 = A090116(n)^2 is the least square that is "surrounded" by two closest primes, by prevprime(x^2) and nextprime(x^2) whose difference nextprime - prevprime = 2n.

4, 9, 25, 361, 144, 625, 121, 1936, 529, 900, 3249, 1681, 2500, 10404, 5776, 10816, 10000, 22201, 30625, 25281, 121104, 76176, 93025, 157609, 212521, 35721, 119025, 1121481, 190969, 672400, 693889, 1004004, 259081, 1646089, 675684, 1207801

Offset

1,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..57

Example

n=5: a(5)=144, primes closest to 144 are {139,149} of which the difference 149 - 139 = 10 = 2n and 144 is the smallest square with this property;
n=1: a(1)=4, 2^2 = 4 is surrounded by {3,5} closest primes with difference 5 - 3 = 2 = 2n.

Mathematica

de[x_ ]:= Prime[PrimePi[x]+1]-Prime[PrimePi[x]] t=Table[de[w^2], {w, 1, 50000}]; q=Table[Min[Flatten[Position[t, 2*j]]]^2, {j, 1, 100}]
Table[Min[Transpose[Select[{#, NextPrime[#]-NextPrime[#, -1]}&/@ (Range[ 2, 5000]^2), Last[#]==2n&]][[1]]], {n, 40}] (* Harvey P. Dale, Sep 04 2011 *)

Crossrefs

Cf. A090116, A090117, A090118, A090119.

Sequence in context: A191273 A087361 A340642 * A329125 A020181 A216134

Adjacent sequences: A090114 A090115 A090116 * A090118 A090119 A090120

Keyword

nonn

Author

Labos Elemer, Jan 09 2004

Status

approved