

A087126


Primes of the form p^k  p^(k1) + 1 for some prime p and integer k > 1.


3



3, 5, 7, 17, 19, 43, 101, 157, 163, 257, 487, 1459, 2029, 4423, 6163, 14407, 19183, 22651, 23549, 26407, 37057, 39367, 62501, 65537, 77659, 113233, 121453, 143263, 208393, 292141, 342733, 375157, 412807, 527803, 564899, 590593, 697049, 843643
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OFFSET

1,1


COMMENTS

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^(k1) is for n = p^k. However, this is not true when p^k  p^(k1) + 1 is prime.


LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Eric Weisstein's World of Mathematics, Totient Function
Eric Weisstein's World of Mathematics, Totient Valence Function


MATHEMATICA

lst={}; maxNum=10^6; n=1; While[p=Prime[n]; p^2p+1<maxNum, i=2; While[m=p^ip^(i1)+1; m<maxNum, If[PrimeQ[m], AppendTo[lst, m]]; i++ ]; n++ ]; Sort[lst]


CROSSREFS

Cf. A002383 (primes of the form n^2 + n + 1, which is the same as n^2  n + 1).
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^(k1) + 1 is prime for p = prime(n)).
Sequence in context: A092951 A001259 A248370 * A331800 A062547 A125739
Adjacent sequences: A087123 A087124 A087125 * A087127 A087128 A087129


KEYWORD

nonn


AUTHOR

T. D. Noe, Aug 15 2003


STATUS

approved



