A167768 -id:A167768 - cp's OEIS frontend

A167767 First of 3 or more consecutive integers with equal values of phi(phi(n)).

1, 2, 7, 8, 20, 31, 32, 33, 146, 211, 314, 384, 626, 674, 1754, 2694, 2695, 5186, 11714, 12242, 17329, 17613, 19310, 25544, 35774, 36728, 38018, 40227, 42626, 56834, 65731, 91106, 97724, 110971, 117536, 131071, 131072, 155821, 161734, 164174

Offset: 1

Fred Schneider, Nov 11 2009

Let p2(n) = phi(phi(n)). This list shows numbers n such that p2(n) = p2(n+1) = p2(n+2) = x for some x.

Here phi is Euler's totient function.

			p2(1) = p2(2) = p2(3) = 1, p2(7) = p2(8) = p2(9) = 2.

Donovan Johnson, Table of n, a(n) for n = 1..500

Cf. A167768.

[n: n in [1..2*10^5] | EulerPhi(EulerPhi(n)) eq EulerPhi(EulerPhi(n + 1)) and EulerPhi(EulerPhi(n)) eq EulerPhi(EulerPhi(n + 2))]; // Vincenzo Librandi, Jun 24 2016

Select[Range[100], EulerPhi[EulerPhi[#]] == EulerPhi[EulerPhi[# + 1]] && EulerPhi[EulerPhi[#]] == EulerPhi[EulerPhi[# + 2]] &] (* G. C. Greubel, Jun 23 2016 *)
SequencePosition[EulerPhi[EulerPhi[Range[170000]]],{x_,x_,x_}][[;;, 1]] (* Harvey P. Dale, Sep 02 2025 *)

isok(n) = (eulerphi(eulerphi(n)) == eulerphi(eulerphi(n+1))) && (eulerphi(eulerphi(n)) == eulerphi(eulerphi(n+2))) \\ Michel Marcus, Jul 12 2013

{n: A010554(n) = A010554(n+1) = A010554(n+2)}. - R. J. Mathar, Nov 12 2009

Edited by N. J. A. Sloane, Nov 12 2009

Extended by R. J. Mathar, Nov 12 2009

A167781 a(n) = smallest number b such that b+n is the first number after b with phi(phi(b)) = phi(phi(b+n)).

Original entry on oeis.org

1, 4, 45, 14, 58, 25, 68, 17, 183, 41, 27, 85, 274, 101, 875, 38, 184, 53, 478, 196, 848, 807, 23, 173, 615, 125, 271, 303, 189, 351, 405, 191, 1035, 667, 596, 218, 915, 133, 1525, 397, 376, 92, 1191, 449, 3466, 552, 47, 346, 404, 137

Offset: 1

Fred Schneider, Nov 11 2009

Phi is Euler's totient function in this context.

Cf. A167766, A167767, A167768

/* brute force search */ ppu(b)= { filename = "c:/math/ppu.txt"; if (!b,b=100000); v = listcreate(b+1); for(x=1,b,listput(v,eulerphi(eulerphi(x)))); z=b\5; sv = listcreate(z+1); for(y=1,z,listput(sv,0)); ct = 0; for(i=1,b, vi = 1; j= i + vi; noMatch = 1; /*print("Here is ",i," and ",v[i]);*/ while( (noMatch==1) && (vi < z) && (j < b), if (v[i]==v[j], if (sv[vi] == 0, /*print("*** Matching on ",vi," for ",i);*/ sv[vi] = i; ct+=1; ); noMatch = 0; , vi += 1; j += 1 ) ); if(nomatch==1,print(i," couldn't find a match before ",j)) ); for(i=1,z, if (sv[i]!=0, print(i,") ",sv[i]); write(filename,sv[i],",") , return(0)) ) }

Edited by N. J. A. Sloane, Nov 12 2009

cp's OEIS Frontend

A167767 First of 3 or more consecutive integers with equal values of phi(phi(n)).

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