A114141 Difference between first odd semiprime > 3^n and 3^n.

8, 6, 6, 6, 4, 4, 2, 2, 22, 6, 8, 2, 2, 20, 10, 4, 6, 8, 4, 4, 2, 4, 20, 10, 8, 6, 10, 2, 2, 8, 14, 12, 20, 10, 14, 20, 16, 6, 14, 4, 2, 8, 8, 12, 2, 24, 20, 10, 10, 4, 48, 40, 8, 34, 4, 4, 38, 56, 4, 28, 2, 14, 14, 22, 6, 8, 10, 4, 16, 4, 20, 2, 26, 56, 32

Offset: 0

Author

Jonathan Vos Post, Feb 03 2006

Keywords

• easy
• nonn

Comments

A098147 is difference between first odd semiprime > 10^n and 10^n. How can we prove that there exists an a(n) for all n? In this powers of 3 sequence, does 2 occur infinitely often? Does every even integer k > 0 occur?

Examples

			a(0) = 8 because 3^0 + 8 = 9 = 3^2 is an odd semiprime.
a(1) = 6 because 3^1 + 6 = 9 = 3^2 is an odd semiprime.
a(2) = 6 because 3^2 + 6 = 15 = 3 * 5 is an odd semiprime.
a(3) = 6 because 3^3 + 6 = 33 = 3 * 11 is an odd semiprime.
a(4) = 4 because 3^4 + 4 = 85 = 5 * 17 is an odd semiprime.
a(5) = 4 because 3^5 + 4 = 247 = 13 * 19 is an odd semiprime.
		

Crossrefs

Cf. A000244, A001358, A098147.

Programs

Mathematica

a[n_] := Block[{z}, z = 3^n + 2; While[ PrimeOmega[z] != 2, z += 2]; z - 3^n]; a /@ Range[0, 60] (* Giovanni Resta, Jun 14 2016 *)

Formula

a(n) = minimum integer k such that 3^n + k is an element of A046315. a(n) = minimum integer k such that A000244(n) + k is an element of A046315.

Extensions

a(26) corrected and more terms from Giovanni Resta, Jun 14 2016