A090119 a(n) = nextprime(A090117(n)), the smallest prime following squares listed in A090117 and also the distance of a(n) from the preceding prime is 2*n.

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(A090117(n)) = nextprime(A090116(n)^2).

a(n) = A007918(A090117(n)) = prime(1+pi(A090117(n))).

Example

a(7) = 127 because 127-113 = 14 = 2*7 and 121 = 11^2 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]]; de[1] = 0; 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, A090117, 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

Extensions

Name corrected by Jason Yuen, Jun 23 2025

Status

approved