%I A048597
%S A048597 1,2,3,4,6,8,12,18,24,30
%N A048597 Very round numbers: reduced residue system consists of only primes and 
               1.
%C A048597 According to Ribenboim, Schatunowsky and Wolfskehl independently showed 
               that 30 is the largest element in the sequence. This gives a lower 
               bound for the maximum of the smallest prime in a, a+d, a+2d, ... 
               taken over all a with 1 < a < d and GCD(a,d) = 1 for d > 30 [see 
               Ribenboim]
%D A048597 A. H. Beiler, Recreations in the Theory of Numbers, page 91.
%D A048597 R. Honsberger, Mathematical Diamonds, MAA, 2003, see p. 79. [Added by 
               N. J. A. Sloane, Jul 05 2009]
%D A048597 P. Ribenboim: The little book of big primes, Chapter on primes in arithmetic 
               progression
%D A048597 H. Rademacher and O. Toeplitz, Von Zahlen und Figuren, Springer Verlag, 
               Berlin, 1933, Zweite Auflage, see last chapter.
%D A048597 H. Rademacher & O. Toeplitz, The Enjoyment of Mathematics, pp. 187-192 
               Dover NY 1990.
%D A048597 J. E. Roberts, Lure of Integers, pp. 179-180 MAA 1992
%H A048597 Bill Taylor, <a href="http://mathforum.org/epigone/sci.math/chaxclixsnerm">
               Posting to sci.math, Sep 13 1999</a>
%F A048597 PrimeQ[ {k | GCD[ a[ n ], k ]=1; k= 2, ..., n-1} ] = True for all k.
%e A048597 The reduced residue systems of these numbers are as follows: {{1, {1}}, 
               {2, {1}}, {3, {1, 2}}, {4, {1, 3}}, {6, {1, 5}}, {8, {1, 3, 5, 7}}, 
               {12, {1, 5, 7, 11}}, {18, {1, 5, 7, 11, 13, 17}}, {24, {1, 5, 7, 
               11, 13, 17, 19, 23}}, {30, {1, 7, 11, 13, 17, 19, 23, 29}}}
%Y A048597 The sequences consists of the n with A036997(n)=0.
%Y A048597 Sequence in context: A107368 A074733 A001461 this_sequence A074964 A017822 
               A156082
%Y A048597 Adjacent sequences: A048594 A048595 A048596 this_sequence A048598 A048599 
               A048600
%K A048597 fini,full,nonn
%O A048597 1,2
%A A048597 Labos E. (labos(AT)ana.sote.hu)
%E A048597 Additional comments from Ulrich Schimke (ulrschimke(AT)aol.com), May 
               29 2001.