A007379 Earliest sequence with a(a(n)) = 4n.

0, 2, 4, 5, 8, 12, 7, 24, 16, 10, 36, 13, 20, 44, 15, 56, 32, 18, 68, 21, 48, 76, 23, 88, 28, 26, 100, 29, 96, 108, 31, 120, 64, 34, 132, 37, 40, 140, 39, 152, 144, 42, 164, 45, 52, 172, 47, 184, 80, 50, 196, 53, 176, 204, 55, 216, 60, 58, 228, 61, 224, 236, 63, 248

Offset: 0

Author

Colin Mallows, N. J. A. Sloane, Mira Bernstein

Keywords

• nonn
• nice

References

• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• T. D. Noe, Table of n, a(n) for n = 0..1000
• Index entries for sequences of the a(a(n)) = 2n family

Crossrefs

Cf. A002516, A002517.

Programs

Mathematica

a[n_] := a[n] = Which[ Mod[n, 8] == 0, 4*a[n/4], Mod[n, 8] == 1, n+1, Mod[n, 8] == 2, 4*(n-2)+4, Mod[n, 8] == 3, n+2, Mod[n, 8] == 4, 4*a[(n-4)/4+1], Mod[n, 8] == 5, 4*(n-5) + 12, Mod[n, 8] == 6, n+1, True, 4*(n-7)+24]; a[0] = 0; Table[ a[n], {n, 0, 63}] (* Jean-François Alcover, Sep 24 2012 *)

Formula

a(8n)=4*a(2n), a(8n+1)=8n+2, a(8n+2)=32n+4, a(8n+3)=8n+5, a(8n+4)=4*a(2n+1), a(8n+5)=32n+12, a(8n+6)=8n+7, a(8n+7)=32n+24

Extensions

Formula and more terms from Henry Bottomley, Apr 27 2000