A320391 Numbers k such that phi(k - 2) = phi(k) - 2.
5, 7, 8, 13, 14, 16, 19, 20, 22, 31, 43, 46, 61, 64, 73, 94, 103, 109, 118, 139, 151, 166, 181, 193, 199, 214, 229, 241, 256, 271, 283, 313, 334, 349, 358, 421, 433, 454, 463, 523, 526, 571, 601, 619, 643, 661, 694, 718, 766, 811, 823, 829, 859, 883, 934, 958
Offset: 1
Keywords
Examples
7 is in the sequence because phi(5) = 4 = phi(7) - 2. 8 is in the sequence because phi(6) = 2 = phi(8) - 2. 9 is not in the sequence because phi(7) = 6 but phi(9) - 2 = 4 instead.
Links
- Robert Israel, Table of n, a(n) for n = 1..10000
Programs
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GAP
Filtered([1..960],k->Phi(k-2)=Phi(k)-2); # Muniru A Asiru, Oct 28 2018
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Magma
[n: n in [3..1000] | EulerPhi(n-2) eq EulerPhi(n)-2];
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Maple
with(numtheory): select(k->phi(k-2)=phi(k)-2,[$1..960]); # Muniru A Asiru, Oct 28 2018
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Mathematica
Select[Range@1000, EulerPhi@(# - 2) == EulerPhi[#] - 2 &] Flatten[Position[Partition[EulerPhi[Range[1000]],3,1],?(#[[1]]==#[[3]]-2&),1,Heads->False]]+2 (* _Harvey P. Dale, Oct 24 2020 *)
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PARI
isok(n) = eulerphi(n-2) == eulerphi(n)-2; \\ Michel Marcus, Oct 14 2018
Formula
a(n) = A001838(n)+2. - Robert Israel, Oct 30 2018