A078776 -id:A078776 - cp's OEIS frontend

A327880 Numbers k such that phi(k) < phi(k+1) < phi(k+2) < phi(k+3) where phi is the Euler totient function (A000010).

1484, 2534, 3002, 3674, 3926, 4454, 4484, 4784, 4844, 5264, 5312, 5984, 6104, 7994, 8294, 8414, 8774, 8834, 9074, 9164, 9944, 10004, 10724, 11024, 11684, 11894, 12254, 13034, 13064, 13166, 13454, 13754, 14234, 15344, 15554, 16184, 16214, 16814, 17384, 17534

Offset: 1

Amiram Eldar, Sep 28 2019

nonn

			1484 is in the sequence since phi(1484) = 624, phi(1485) = 720, phi(1486) = 742, and phi(1487) = 1486, and 624 < 720 < 742 < 1486.

Jean-Marie De Koninck, Those Fascinating Numbers, American Mathematical Society, 2009, p. 34, entry 105 and p. 130, entry 1484.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A000010, A078776, A161962.

aQ[n_] := AllTrue[Differences @ EulerPhi[n + Range[0, 3]], # > 0 &]; Select[Range[18000], aQ]

ok(k)={for(i=0, 2, if(eulerphi(k+i) >= eulerphi(k+i+1), return(0))); 1}
{ select(ok, [1..20000]) } \\ Andrew Howroyd, Sep 28 2019

A326817 Numbers k such that phi(k) > phi(k+1) > phi(k+2) > phi(k+3) where phi is the Euler totient function (A000010).

Original entry on oeis.org

823, 943, 3133, 4387, 4873, 5443, 5563, 5863, 7213, 7753, 7873, 8383, 9007, 10333, 10693, 11113, 11503, 12043, 12763, 13483, 13843, 13921, 14623, 14683, 16573, 16663, 16963, 16993, 17113, 17983, 19003, 19093, 19303, 20083, 20143, 20953, 21613, 21733, 22513

Offset: 1

Kritsada Moomuang, Oct 20 2019

nonn

			823 is in the sequence since phi(823) = 822, phi(824) = 408, phi(825) = 400, phi(826) = 348, and 822 > 408 > 400 > 348.

Jean-Marie De Koninck, Those Fascinating Numbers, American Mathematical Society, 2009, page 106, entry 823.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A000010, A078776, A161962, A161963, A206581, A327880.

Subsequence of A328056.

aQ[n_] := AllTrue[Differences @ EulerPhi[n + Range[0, 3]], # < 0 &]; Select[Range[23000], aQ] (* Amiram Eldar, Oct 20 2019 *)

A328056 Numbers k such that phi(k) > phi(k+1) > phi(k+2) where phi is the Euler totient function (A000010).

Original entry on oeis.org

313, 523, 733, 823, 824, 943, 944, 973, 1153, 1363, 1573, 1753, 1783, 1813, 1993, 2143, 2413, 2473, 2623, 2803, 3043, 3133, 3134, 3253, 3313, 3463, 3703, 3883, 4093, 4123, 4303, 4387, 4388, 4513, 4723, 4873, 4874, 4933, 5113, 5143, 5353, 5443, 5444, 5563, 5564

Offset: 1

Kritsada Moomuang, Oct 03 2019

nonn

Contains all members k of A206581 such that k==103 (mod 210) except 103.- Robert Israel, Oct 16 2019

			313 is in the sequence since phi(313) = 312, phi(314) = 156, phi(315) = 144, and 312 > 156 > 144.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A000010, A078776, A161962, A161963, A206581, A327880.

Supersequence of A326817.

[k:k in [1..5600]| EulerPhi(k) gt EulerPhi(k+1) and EulerPhi(k+1) gt EulerPhi(k+2)]; // Marius A. Burtea, Oct 07 2019

R:= NULL: count:= 0:
q:= false: s:= 0:
for i from 1 while count < 100 do
  t:= numtheory:-phi(i);
  r:= q;
  q:= evalb(tRobert Israel, Oct 16 2019

Flatten[Position[Partition[EulerPhi[Range[5600]], 3, 1], ?(Max[Differences[#]] < 0 &)] // Quiet] (* _Amiram Eldar, Oct 06 2019 after Harvey P. Dale at A078776 *)

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A327880 Numbers k such that phi(k) < phi(k+1) < phi(k+2) < phi(k+3) where phi is the Euler totient function (A000010).

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A326817 Numbers k such that phi(k) > phi(k+1) > phi(k+2) > phi(k+3) where phi is the Euler totient function (A000010).

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A328056 Numbers k such that phi(k) > phi(k+1) > phi(k+2) where phi is the Euler totient function (A000010).

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