A134765 Least prime p for which (p-1)/2 - phi(p-1) = n, or 0 if there is no such prime.

3, 7, 13, 19, 41, 0, 37, 31, 113, 43, 101, 71, 73, 67, 61, 79, 97, 131, 109, 103, 0, 0, 0, 191, 0, 139, 677, 127, 0, 419, 157, 0, 193, 0, 0, 151, 0, 0, 0, 199, 401, 683, 181, 0, 281, 0, 0, 431, 0, 283, 277, 0, 0, 659, 461, 0, 241, 211, 0, 743, 313, 0, 349, 271, 641, 827

Offset: 0

Author

T. D. Noe, Nov 13 2007, Nov 19 2007

Keywords

• nonn

Comments

The graph of this sequence shows that for n>8 either a(n)=0 or a(n)<=1+n^2. See A098006 for the values of (p-1)/2 - phi(p-1) for odd primes p. Sequence A098047 lists the n for which a(n)=0. A134854(n)=a(2^(n-1)).

Links

• T. D. Noe, Table of n, a(n) for n = 0..10000
• T. D. Noe, Finding primes p for which (p-1)/2 - phi(p-1) = k
• T. D. Noe, Graph for n <= 50000

Programs

Mathematica

nn=1000; lc=Table[0,{nn}]; Do[p=Prime[n]; r=(p-1)/2-EulerPhi[p-1]; If[0