A256417 The EKG sequence (A064413) smoothed by replacing each prime p with 2p and each thrice-prime 3p also with 2p.

1, 4, 4, 4, 6, 6, 12, 8, 10, 10, 10, 18, 14, 14, 14, 24, 16, 20, 22, 22, 22, 27, 30, 25, 35, 28, 26, 26, 26, 36, 32, 34, 34, 34, 42, 38, 38, 38, 45, 40, 44, 46, 46, 46, 48, 50, 52, 54, 56, 49, 63, 60, 55, 65, 70, 58, 58, 58, 66, 62, 62

Offset

1,2

Comments

This smoothing of A064413 is discussed in Lagarias et al. (2002).

a(n) = A256415(A064413(n)). - Reinhard Zumkeller, Apr 06 2015

Links

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

J. C. Lagarias, E. M. Rains and N. J. A. Sloane, The EKG sequence, arXiv:math/0204011 [math.NT], 2002.

J. C. Lagarias, E. M. Rains and N. J. A. Sloane, The EKG Sequence, Exper. Math. 11 (2002), 437-446.

Mathematica

ekg[s_] := Block[{m = s[[-1]], k = 3}, While[MemberQ[s, k] || GCD[m, k] == 1, k++]; Append[s, k]];
Nest[ekg, {1, 2}, 100] /. {n_ /; PrimeQ[n] -> 2n, n_ /; PrimeQ[n/3] -> 2n/3 } (* Jean-François Alcover, Aug 04 2018, after Robert G. Wilson v *)

Prog

(Haskell)
a256417 = a256415 . a064413  -- Reinhard Zumkeller, Apr 06 2015

Crossrefs

Cf. A064413, A256415, A256416.

Sequence in context: A219760 A097918 A256416 * A229630 A141466 A171743

Adjacent sequences: A256414 A256415 A256416 * A256418 A256419 A256420

Keyword

nonn

Author

N. J. A. Sloane, Apr 05 2015

Status

approved