A114313 Difference between first odd semiprime >= 5^n and 5^n.

8, 4, 0, 4, 4, 2, 2, 2, 4, 4, 2, 2, 4, 14, 4, 2, 18, 6, 2, 12, 16, 2, 4, 2, 42, 6, 4, 2, 22, 26, 12, 18, 18, 38, 12, 14, 2, 6, 36, 2, 16, 24, 6, 14, 12, 6, 28, 24, 24, 8, 16, 32, 16, 28, 12, 8, 16, 6, 16, 98

Offset: 0

Author

Jonathan Vos Post, Feb 05 2006

Keywords

• easy
• nonn

Comments

A098147 is difference between first odd semiprime > 10^n and 10^n.

Examples

			a(0) = 8 because 5^0 + 8 = 9 = 3^2 is an odd semiprime; note that because 5^0 + 3 = 4 = 2^2 is an even semiprime, but we only care about odd semiprimes here.
a(1) = 4 because 5^1 + 4 = 9 = 3^2 is an odd semiprime.
a(2) = 0 because 5^2 + 0 = 25 = 5^2 is an odd semiprime; there are no more zero values.
a(3) = 4 because 5^3 + 4 = 129 = 3 * 43.
a(4) = 4 because 5^4 + 4 = 629 = 17 * 37.
a(5) = 2 because 5^5 + 2 = 3127 = 53 * 59.
a(6) = 2 because 5^6 + 2 = 15627 = 3 * 5209.
a(7) = 2 because 5^7 + 2 = 78127 = 7 * 11161.
a(8) = 4 because 5^8 + 4 = 390629 = 577 * 677 (brilliant).
a(9) = 4 because 5^9 + 4 = 1953129 = 3 * 651043.
		

Crossrefs

Cf. A000351, A001358, A098147.

Programs

Mathematica

dfpsn[n_]:=Module[{n5=5^n,s},s=If[OddQ[n5],n5,n5+1];While[PrimeOmega[s] != 2,s=s+2];s-n5]; Array[dfpsn,60,0] (* Harvey P. Dale, Sep 04 2013 *)

Formula

a(n) = minimum integer k such that 5^n + k is an element of A046315. a(n) = minimum integer k such that A000351(n) + k is an element of A046315.

Extensions

Corrected and extended by Harvey P. Dale, Sep 04 2013