A295865 Numbers k, the smallest of at least 4 consecutive numbers x, for which phi(x) <= phi(x+1).

1, 2, 14, 104, 164, 254, 494, 584, 1484, 2204, 2534, 2834, 3002, 3674, 3926, 4454, 4484, 4784, 4844, 5186, 5264, 5312, 5984, 6104, 7994, 8294, 8414, 8774, 8834, 9074, 9164, 9944, 10004, 10604, 10724, 11024, 11684, 11894, 12254, 13034, 13064, 13166, 13364, 13454, 13754, 14234, 15344, 15554, 16184, 16214

Offset

1,2

Comments

There are 3988536 terms below 2*10^9.

Up to a(3988356):

- a(1) is the only odd term.

- a(1) is the only term with 5 consecutive numbers where phi(k) <= phi(k+1).

- the only powers of 2 are a(1)=1 and a(2) = 2.

- of the residues of a(n) mod 10, 4 accounts for greater than 91%.

- if a(n) is divisible by 4, then phi(a(n)) is divisible by 4.

Numbers k such that A057000(k) >= 0 for 3 consecutive terms. - Michel Marcus, Mar 21 2018

Links

Table of n, a(n) for n=1..50.

Example

14 is a term because phi(14) <= phi(15) <= phi(16) <= phi(17).
15 is not a term because phi(15) <= phi(16) <= phi(17) > phi(18).

Maple

Phi:= map(numtheory:-phi, [$1..20001]):
DPhi:= Phi[2..-1]-Phi[1..-2]:
C:= select(t -> DPhi[t]>=0, [$1..20000]):
C[select(t -> C[t+2]=C[t]+2, [$1..nops(C)-3])]; # Robert Israel, Mar 26 2018

Mathematica

Drop[#, -2] & /@ Select[SplitBy[#, Last@ # >= 0 &], Length@ # > 2 && #[[1, -1]] >= 0 &][[All, All, 1]] &@ MapIndexed[{First@ #2, #1} &, Differences@ Array[EulerPhi, 2^14]] // Flatten (* Michael De Vlieger, Mar 26 2018 *)

Prog

(PARI) isok(n) = {my(v = vector(4, k, eulerphi(n+k-1))); (v[1] <= v[2]) && (v[2] <= v[3]) && (v[3] <= v[4]); } \\ Michel Marcus, Mar 21 2018

Crossrefs

Cf. A000010, A057000.

Sequence in context: A085372 A123525 A286310 * A355069 A378611 A293044

Adjacent sequences: A295862 A295863 A295864 * A295866 A295867 A295868

Keyword

nonn

Author

Torlach Rush, Feb 13 2018

Status

approved