A090118 a(n) = prevprime(A090117(n)), the largest prime previous to squares given in A090117, being such that distance of a(n) to the following prime equals 2*n.

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

Author

Labos Elemer, Jan 09 2004

Keywords

• nonn

Examples

			a(7) = 113 because 127-113 = 14 = 2*7 and 121 = 11^2 is between {127,113} closest primes; also 113 is the smallest prime with this property.
		

Crossrefs

Cf. A090116, A090117, A090119.

Programs

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[pre[Part[mt, j]^2], {j, 1, Length[mt]}]

Formula

a(n) = prevprime(A090117(n)) = prevprime(A090116(n)^2).

a(n) = prime(pi(A090117(n))).

Extensions

Name corrected by Jason Yuen, Jun 23 2025