A076665 Numbers k such that phi(k) + phi(k+3) = phi(k+1) + phi(k+2).

1, 5, 7, 11, 17, 22, 88, 292, 847, 1337, 1691, 7367, 10385, 15430, 51215, 93401, 132535, 211817, 282725, 358852, 359905, 382955, 486772, 507725, 580262, 664870, 700532, 1691081, 1972691, 2637712, 5154625, 5886265, 6510485, 13841531

Offset

1,2

Comments

Each term of the sequence marks the start of four consecutive phi-values for which the sum of the means equals the sum of the extremes.

Links

Amiram Eldar, Table of n, a(n) for n = 1..100 (terms 1..44 from M. F. Hasler)

Example

phi(7) + phi(10) = 6 + 4 = 10; phi(8) + phi(9) = 4 + 6 = 10, so 7 is a term of the sequence.

Mathematica

Select[Range[10^5], EulerPhi[ # ] + EulerPhi[ # + 3] == EulerPhi[ # + 1] + EulerPhi[ # + 2] &]
Flatten[Position[Partition[EulerPhi[Range[14*10^6]], 4, 1], _?(#[[1]]+ #[[4]] == #[[2]]+#[[3]]&), {1}, Heads->False]] (* Harvey P. Dale, Dec 12 2015 *)

Prog

(PARI) t=vector(4, i, i)~; c=[[1, 1, -1, -1], [1, -1, -1, 1]]; for(n=1, 10^9, t[n%4+1]=eulerphi(n); c[n%2+1]*t & next; print1(n-3, ", ")) \\ M. F. Hasler, Feb 07 2009
(Magma) [k: k in [1..10^5] |EulerPhi(k)+EulerPhi(k+3)-EulerPhi(k+1)-EulerPhi(k+2)eq 0]; // Marius A. Burtea, Oct 02 2019

Crossrefs

Sequence in context: A271658 A282739 A072249 * A124598 A096215 A144742

Adjacent sequences: A076662 A076663 A076664 * A076666 A076667 A076668

Keyword

nonn

Author

Joseph L. Pe, Oct 25 2002

Extensions

Terms beyond a(16) from M. F. Hasler, Feb 07 2009

Status

approved