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%I #8 Jul 16 2012 12:10:23
%S 3,5,7,17,19,43,101,157,163,257,487,1459,2029,4423,6163,14407,19183,
%T 22651,23549,26407,37057,39367,62501,65537,77659,113233,121453,143263,
%U 208393,292141,342733,375157,412807,527803,564899,590593,697049,843643
%N Primes of the form p^k - p^(k-1) + 1 for some prime p and integer k > 1.
%C It is usually the case that, for prime p and k > 1, the first time the totient function phi(n) has value p^k - p^(k-1) is for n = p^k. However, this is not true when p^k - p^(k-1) + 1 is prime.
%H Vincenzo Librandi, <a href="/A087126/b087126.txt">Table of n, a(n) for n = 1..1000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/TotientFunction.html">Totient Function</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/TotientValenceFunction.html">Totient Valence Function</a>
%t lst={}; maxNum=10^6; n=1; While[p=Prime[n]; p^2-p+1<maxNum, i=2; While[m=p^i-p^(i-1)+1; m<maxNum, If[PrimeQ[m], AppendTo[lst, m]]; i++ ]; n++ ]; Sort[lst]
%Y Cf. A002383 (primes of the form n^2 + n + 1, which is the same as n^2 - n + 1).
%Y Cf. A019434 (Fermat primes), A003306 (2*3^n + 1 is prime), A056799 (8*9^n + 1 is prime), A056797 (9*10^n + 1 is prime), A087139 (least k such that p^k - p^(k-1) + 1 is prime for p = prime(n)).
%K nonn
%O 1,1
%A _T. D. Noe_, Aug 15 2003
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