A090119 a(n)=nextprime[A090116(n)], the smallest prime following squares listed in A090116 and also the distance of a(n) from the preceding prime is 2n.

5, 11, 29, 367, 149, 631, 127, 1949, 541, 907, 3251, 1693, 2503, 10427, 5779, 10831, 10007, 22229, 30631, 25301, 121123, 76207, 93047, 157627, 212557, 35729, 119027, 1121509, 190979, 672439, 693943, 1004027, 259099, 1646101, 675713, 1207841

Offset

1,1

Links

Table of n, a(n) for n=1..36.

Formula

a(n) = nextprime[A090116(n)^2] = nextprime[A090117(n)] = p[1+pi[A090117(n)]] = A007918[A090116[n]].

Example

n=7: a(7)=127 because 127-113=14=2.7 and 121=11 is between {127,113} closest primes to 121 a suitable square number. Also 127 is the smallest prime with this property.

Mathematica

pre[x_ := Prime[PrimePi[x]] nex[x_ := Prime[PrimePi[x]+1] de[x_ := Prime[PrimePi[x]+1]-Prime[PrimePi[x]] t=Table[de[w^2], {w, 1, 50000}]; mt=Table[Min[Flatten[Position[t, 2*j]]], {j, 1, 100}] Table[nex[Part[mt, j]^2], {j, 1, Length[mt]}]

Crossrefs

Cf. A090116-A090118, A007917, A007918, A000720, A000040, A053001, A007491, A000290.

Sequence in context: A053185 A358900 A337394 * A174922 A088484 A179256

Adjacent sequences: A090116 A090117 A090118 * A090120 A090121 A090122

Keyword

nonn

Author

Labos Elemer, Jan 09 2004

Status

approved