A090118 a(n)=prevprime[A090116(n)], the largest prime previous to squares given in A090116, being such that distance of a(n) to the following prime equals 2n.

3, 7, 23, 359, 139, 619, 113, 1933, 523, 887, 3229, 1669, 2477, 10399, 5749, 10799, 9973, 22193, 30593, 25261, 121081, 76163, 93001, 157579, 212507, 35677, 118973, 1121453, 190921, 672379, 693881, 1003963, 259033, 1646033, 675643, 1207769

Offset

1,1

Links

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

Formula

a(n)=prevprime[A090116(n)^2]-prevprime[A090117(n)]=p[pi[A090117(n)]]

Example

n=7: a(7)=113 because 127-113=14=2.7 and 121=11 is
between {127,113} closest primes; also 113 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[pre[Part[mt, j]^2], {j, 1, Length[mt]}]

Crossrefs

Cf. A090116-A090119.

Sequence in context: A090188 A001773 A067604 * A099183 A316792 A358974

Adjacent sequences: A090115 A090116 A090117 * A090119 A090120 A090121

Keyword

nonn

Author

Labos Elemer, Jan 09 2004

Status

approved