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.
%I A087139 #12 Mar 31 2012 10:30:04
%S A087139 2,2,3,2,11,2,5,30,15,3,6,10,81,3,17,961,15,7,2,5,6,2,3,3,12,3,57,5,
%T A087139 16,5,166,15,13,2,3,2,30,2,25,3,47,3,3,2,521,9,3,15,17,42,17,51,39
%N A087139 Least k>1 such that p^k - p^(k-1) + 1 is prime for p = prime(n).
%C A087139 The next term in this sequence, a(54) for the prime p=251, is greater than 73000.
%C A087139 Is there a prime p such that p^k - p^(k-1) + 1 is composite for all k > 1? For the related question of Sierpinski numbers (n such that n*2^k+1 is composite for all k ), the answer is yes.
%C A087139 If n=251^k-251^(k-1)+1 is prime then k mod 10 = 1,5,7 or 9 because n mod 3 = 0 iff k is even and n mod 11 = 0 iff k mod 5 = 3. More exponents can be cleared this way. - _Bernardo Boncompagni_, Oct 23 2005
%C A087139 Note that k cannot be 8, 14, 20, ... (i.e. k == 2 mod 6) because then p^2 - p + 1 divides p^k - p^(k-1) + 1. - _T. D. Noe_, Aug 31 2006
%D A087139 See A087126.
%t A087139 lst={}; Do[p=Prime[n]; i=2; While[m=p^i-p^(i-1)+1; !PrimeQ[m], i++ ]; AppendTo[lst, i], {n, 53}]; lst
%Y A087139 Cf. A040076 (Sierpinski numbers), A087126 (primes of the form p^k - p^(k-1) + 1).
%Y A087139 Cf. A122396.
%K A087139 more,nonn
%O A087139 1,1
%A A087139 _T. D. Noe_, Aug 18 2003