A073783 First differences of composite numbers.

2, 2, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 2, 2, 1

Offset: 1

Author

Lior Manor, Aug 11 2002

Keywords

• easy
• nonn

Comments

Also, the highest common factors of pair of successive composite numbers. - Amarnath Murthy, Jan 31 2003

All terms are 1 or 2. Runs of 1's may be of arbitrary lengths, while the lengths of runs of 2's are 1 or 2. - Zak Seidov, Mar 18 2013

Examples

			a(7) = A002808(8) - A002808(7) = 15 - 14 = 1.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A002808, A073784.

a(n) = A136527(n, n+1).

Cf. A073445 (first differences).

Programs

Haskell

a073783 n = a073783_list !! (n-1)
a073783_list = zipWith (-) (tail a002808_list) a002808_list
-- Reinhard Zumkeller, Jan 10 2013

Mathematica

c[x_] := FixedPoint[x + PrimePi[#] + 1 &, x]; Differences[c /@ Range[106]] (* Jayanta Basu, Jul 09 2013 *)

PARI

m=4;forcomposite(n=6,1e3,print1(n-m", ");m=n) \\ Charles R Greathouse IV, Mar 20 2013

Formula

a(n) = A002808(n+1) - A002808(n).

a(n) = A073784(n) + 1.