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

1,1

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

Links

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

Formula

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

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

Conjecture: a(n) = A065310(n+1). - R. J. Mathar, Jul 17 2026

Example

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

Mathematica

c[x_] := FixedPoint[x + PrimePi[#] + 1 &, x]; Differences[c /@ Range[106]] (* Jayanta Basu, Jul 09 2013 *)
(* Alternative: *)
Differences[Select[Range[200], CompositeQ]] (* Paolo Xausa, Jul 17 2026 *)

Prog

(Haskell)
a073783 n = a073783_list !! (n-1)
a073783_list = zipWith (-) (tail a002808_list) a002808_list
-- Reinhard Zumkeller, Jan 10 2013
(PARI) m=4; forcomposite(n=6, 1e3, print1(n-m", "); m=n) \\ Charles R Greathouse IV, Mar 20 2013

Crossrefs

Cf. A002808, A073784.

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

Cf. A073445 (second differences).

Sequence in context: A331104 A270646 A293540 * A134430 A130658 A014695

Adjacent sequences: A073780 A073781 A073782 * A073784 A073785 A073786

Keyword

easy,nonn,changed

Author

Lior Manor, Aug 11 2002

Status

approved