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

1,1

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

Formula

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

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

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 *)

Prog

(Scheme, two alternatives)
(define (A257244 n) (- (A256393 (+ n 1)) (A256393 n)))
(define (A257244 n) (gcd (A256393 (+ n 1)) (A256393 n)))
(Haskell)
a257244 n = a257244_list !! (n-1)
a257244_list = zipWith gcd a256393_list $ tail a256393_list
-- Reinhard Zumkeller, May 06 2015

Crossrefs

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

Cf. A256393.

Sequence in context: A072375 A340500 A131981 * A130147 A345377 A096143

Adjacent sequences: A257241 A257242 A257243 * A257245 A257246 A257247

Keyword

nonn

Author

Antti Karttunen, Apr 19 2015

Status

approved