A353347 Numbers k such that the elements of the continued fraction of phi(k)/k and phi(k+1)/(k+1) are anagrams of each other.

1287, 96074, 5600160, 18486908, 41746312, 78700687, 211818591, 346666215, 535185325, 600248114, 617086359, 682116194, 972901517, 1326113558, 1397946770, 1404159416, 1785588903, 2090593128, 2286664100, 2349999964, 2396173329, 3154287487, 4029358361, 5401346573

Offset

1,1

Links

Table of n, a(n) for n=1..24.

Example

1287 is a term since the sequences of elements of the continued fractions of phi(1287)/1287 = 80/143 and phi(1288)/1288 = 66/161, {0, 1, 1, 3, 1, 2, 2, 2} and {0, 2, 2, 3, 1, 1, 1, 2} respectively, are anagrams of each other.

Mathematica

r[n_] := Sort[ContinuedFraction[EulerPhi[n]/n]]; seq[max_] := Module[{s = {}, n = 2, c = 0, r1 = r[1], r2}, While[n < max, r2 = r[n]; If[r1 == r2, AppendTo[s, n - 1]]; r1 = r2; n++]; s]; seq[6*10^6]

Crossrefs

Cf. A000010 (phi), A069567, A076512, A109395, A342866, A353345, A353346.

Sequence in context: A252116 A084803 A104399 * A232253 A140914 A239436

Adjacent sequences: A353344 A353345 A353346 * A353348 A353349 A353350

Keyword

nonn

Author

Amiram Eldar, Apr 15 2022

Status

approved