cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-2 of 2 results.

A167768 First of 4 or more consecutive integers with equal values of phi(phi(n)).

Original entry on oeis.org

1, 7, 31, 32, 2694, 131071, 50802031105
Offset: 1

Views

Author

Fred Schneider, Nov 11 2009

Keywords

Comments

Next term > 1266046940 (last term of A167767 b-file). - Michel Marcus, Jun 23 2013
No other terms < 1.32*10^12. - Jud McCranie, Jul 19 2017

Examples

			p2(1) = p2(2) = p2(3) = p2(4) = 1, p2(7) = p2(8) = p2(9) = p2(10) = 2.

Crossrefs

Cf. A167767 (of which this list is a subset), A167766.

Programs

  • Mathematica
    a[n_] := EulerPhi[EulerPhi[n]]; Select[Range[10000], a[#] == a[# + 1] && a[# + 1] == a[# + 2] && a[# + 2] == a[# + 3] &] (* G. C. Greubel, Jun 23 2016 *)
  • PARI
    pp(n) = eulerphi(eulerphi(n))
isA167768(n) = pp(n)==pp(n+1) && pp(n+1)==pp(n+2) && pp(n+2)==pp(n+3) \\ Michael B. Porter, Nov 24 2009

Extensions

Edited by N. J. A. Sloane, Nov 12 2009
a(7) added by Jud McCranie, Jul 17 2017

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

Views

Author

Fred Schneider, Nov 11 2009

Keywords

Comments

Phi is Euler's totient function in this context.

Crossrefs

Cf. A167766, A167767, A167768

Programs

  • PARI
    /* 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)) ) }

Extensions

Edited by N. J. A. Sloane, Nov 12 2009
Showing 1-2 of 2 results.

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