A174254 p-x^x where p is prime number and x is largest integer such that x^x is smaller than p.

1, 2, 1, 3, 7, 9, 13, 15, 19, 2, 4, 10, 14, 16, 20, 26, 32, 34, 40, 44, 46, 52, 56, 62, 70, 74, 76, 80, 82, 86, 100, 104, 110, 112, 122, 124, 130, 136, 140, 146, 152, 154, 164, 166, 170, 172, 184, 196, 200, 202, 206, 212, 214, 224, 1, 7, 13, 15, 21, 25, 27, 37, 51, 55, 57

Offset

1,2

Comments

1^1=1;2-1=1,3-1=2, 2^2=4;5-4=1,7-4=3,11-4=7,13-4=9,...3^3=27;29-27=2,31-27=4,..

Links

Table of n, a(n) for n=1..65.

Mathematica

f[n_]:=Module[{k=1}, While[n>k^k, ++k]; k-1]; Table[p=Prime[n]; a=f[p]; Prime[n]-a^a, {n, 6!}]
xn[n_]:=Module[{x=Floor[Log[n]/ProductLog[Log[n]]]}, n-x^x]; xn/@Prime[ Range[ 70]] (* Harvey P. Dale, Oct 15 2015 *)

Crossrefs

Cf. A000040, A000312

Sequence in context: A174400 A178079 A258987 * A024404 A077173 A063509

Adjacent sequences: A174251 A174252 A174253 * A174255 A174256 A174257

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Mar 13 2010

Status

approved