A286289 Least number to start a run of exactly n nondecreasing values of the Euler phi function (A000010).

314, 6, 315, 14, 1

Offset

1,1

Comments

a(6) > 10^7. - Michael De Vlieger, May 19 2017

a(6) > 10^13. - Giovanni Resta, Nov 12 2019

References

M. F. Hasler, Posting to Sequence Fans Mailing List, May 06 2017

Links

Table of n, a(n) for n=1..5.

Example

From Michael De Vlieger, May 19 2017: (Start)
A run of subsequent numbers with nondecreasing phi is of length 1 if it consists of a single number n with phi(n-1) > phi(n) > phi(n+1) (else n belongs to a run of length >= 2). This happens first for a(1) = 314.
Phi(14..18) = (6, 8, 8, 16, 6), therefore the first run of 4 numbers with nondecreasing phi(= A000010) starts at a(4) = 14. (End)

Mathematica

Prepend[#, Module[{k = 2}, While[Sign@ Differences@ EulerPhi[k + {-1, 0, 1}] != {-1, -1}, k++]; k]] &@ Function[s, Function[r, If[Length@ # > 0, #[[1, 1]], -1] &@ Select[s, Length@ # == r &]] /@ Range@ Max@ Map[Length, s]]@ DeleteCases[SplitBy[MapIndexed[Function[k, (2 Boole[#1 <= #2] - 1) k & @@ #1]@ First@ #2 &, Partition[Array[EulerPhi, 10^7], 2, 1]], Sign], w_ /; First@ w < 0] (* Michael De Vlieger, May 19 2017 *)

Crossrefs

Cf. A000010, A284597, A285893, A286287, A286288.

Sequence in context: A164772 A068650 A106156 * A219961 A107116 A107115

Adjacent sequences: A286286 A286287 A286288 * A286290 A286291 A286292

Keyword

nonn,more

Author

N. J. A. Sloane, May 16 2017

Status

approved