

A286289


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


3




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(n1) > 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



