A257244 First differences of A256393: a(n) = A256393(n+1) - A256393(n).

2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 5, 5, 5, 3, 3, 3, 3, 3, 5, 5, 7, 7, 7, 7, 7, 3, 3, 3, 19, 7, 7, 3, 5, 5, 5, 3, 7, 5, 5, 5, 19, 11, 11, 3, 13, 13, 13, 3, 23, 13, 13, 5, 11, 11, 11, 3, 61, 7, 31, 3, 13, 13, 19, 3, 43, 13, 13, 3, 7, 5, 5, 5, 61, 11, 31, 23, 23, 3, 127, 7, 7, 3, 151, 7, 19, 3, 181, 7, 13, 3, 43, 31, 31

Offset: 1

Author

Antti Karttunen, Apr 19 2015

Keywords

• nonn

Comments

Sequence gives the differences between the successive terms of A256393, each difference being equal to their unique shared prime factor.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..4095

Crossrefs

Cf. A257245, A257246 (bisections), A257247 (positions where they coincide).

Cf. A256393.

Programs

Haskell

a257244 n = a257244_list !! (n-1)
a257244_list = zipWith gcd a256393_list $ tail a256393_list
-- Reinhard Zumkeller, May 06 2015

Mathematica

f[n_] := Block[{pf = First /@ FactorInteger@ n},
  If[EvenQ@ n, Max@ pf, Min@ pf]]; s = {2}; lmt = 94; For[k = 2,
k <= lmt, k++, AppendTo[s, s[[k - 1]] + f@ s[[k - 1]]]]; Abs[
Subtract @@@ Partition[s, 2, 1]] (* Michael De Vlieger, Apr 19 2015 *)

Formula

a(n) = A256393(n+1) - A256393(n).

a(n) = gcd(A256393(n+1), A256393(n)).