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

0,1

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

Mathematica

nn=1000; lc=Table[0, {nn}]; Do[p=Prime[n]; r=(p-1)/2-EulerPhi[p-1]; If[0<r<=nn && lc[[r]]==0, lc[[r]]=p], {n, 2, PrimePi[1+nn^2]}]; PrependTo[lc, 3]

Crossrefs

Sequence in context: A350591 A252091 A217035 * A023230 A194581 A106080

Adjacent sequences: A134762 A134763 A134764 * A134766 A134767 A134768

Keyword

nonn

Author

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

Status

approved