A028389 The 5x + 1 sequence beginning at 7.

7, 36, 18, 9, 46, 23, 116, 58, 29, 146, 73, 366, 183, 916, 458, 229, 1146, 573, 2866, 1433, 7166, 3583, 17916, 8958, 4479, 22396, 11198, 5599, 27996, 13998, 6999, 34996, 17498, 8749, 43746, 21873, 109366, 54683, 273416, 136708, 68354, 34177, 170886, 85443, 427216

Offset

0,1

Comments

Starting with 11 leads to 7 after 4 steps (11 -> 56 -> 28 -> 14 -> 7) and therefore essentially the same orbit, cf. A259193. - There is a different notion of "5x+1" map and related sequences, where not only factors of 2, but also factors of 3 are divided out, cf. A057688. - M. F. Hasler, Apr 06 2026

Links

Alois P. Heinz, Table of n, a(n) for n = 0..10000

Formula

a(0) = 7; a(n) = 5*a(n-1) + 1 if a(n-1) is odd, a(n) = a(n-1)/2 otherwise.

a(n) = A259193(n+4) for all n >= 0. - M. F. Hasler, Apr 06 2026

Maple

f := proc(n) option remember; if n = 0 then 7 elif f(n-1) mod 2 = 0 then f(n-1)/2 else 5*f(n-1)+1; fi; end; seq(f(n), n=0..50);

Mathematica

a[0] = 7; a[n_] := a[n] = If[OddQ[a[n-1]], 5 a[n-1] + 1, a[n-1]/2];
a /@ Range[0, 50] (* Jean-François Alcover, Nov 03 2020 *)
NestList[If[OddQ[#], 5#+1, #/2]&, 7, 50] (* Harvey P. Dale, Nov 03 2022 *)

Prog

(PARI) A028389_first(N)=vector(N, i, N=if(i==1, 7, N%2, N*5+1, N/2)) \\ M. F. Hasler, Apr 06 2026

Crossrefs

Cf. A057688, A259193, A259207, A328010, A328011.

Sequence in context: A364454 A197555 A362162 * A041603 A176543 A018199

Adjacent sequences: A028386 A028387 A028388 * A028390 A028391 A028392

Keyword

nonn

Author

N. J. A. Sloane, Dean Hickerson

Extensions

Named edited by Andrew Howroyd, Aug 21 2020

Status

approved