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

Author

N. J. A. Sloane, Apr 05 2015

Keywords

• nonn

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.

Crossrefs

Cf. A064413, A256415, A256416.

Programs

Haskell

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

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 *)