A083534 First difference sequence of A007617. Difference between consecutive values not being in the range of phi (A000010).

2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 1, 1, 2, 1, 1, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 1, 1, 2, 2, 2, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 2, 2, 2, 2, 1, 1, 2, 2, 2, 1, 1, 2, 1, 1, 2, 2, 1, 1, 1, 1, 2, 1, 1, 2, 2, 2, 2

Offset

1,1

Comments

a(n) is either 2 or 1 since odd numbers are in A007619.

If a(n) = 1 then A007619(n+1) is an even number not in the range of phi.

Links

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

Formula

a(n) = A007617(n+1) - A007617(n).

Example

{11,13,14,15,17} are not in the range of phi and the corresponding differences are {2,1,1,2}.

Mathematica

t0[x_] := Table[j, {j, 1, x}]; t=Table[EulerPhi[w], {w, 1, 10000}]; u=Union[%]; c=Complement[t0[10000], u]; Delete[c-RotateRight[c], 1]

Prog

(Haskell)
a083534 n = a083534_list !! (n-1)
a083534_list = zipWith (-) (tail a007617_list) a007617_list
-- Reinhard Zumkeller, Nov 26 2015
(PARI) list(lim) = {my(k1 = 3, k2 = 3); while(k1 < lim, until(!istotient(k2), k2++); print1(k2 - k1, ", "); k1 = k2); } \\ Amiram Eldar, Feb 22 2025

Crossrefs

Cf. A000010, A002202, A005277, A007617, A007619, A083531, A083532, A083533, A083535, A083536.

Sequence in context: A373360 A037813 A159700 * A174664 A027386 A102300

Adjacent sequences: A083531 A083532 A083533 * A083535 A083536 A083537

Keyword

nonn,changed

Author

Labos Elemer, May 20 2003

Status

approved