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A048597
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Very round numbers: reduced residue system consists of only primes and 1.
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24
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OFFSET
| 1,2
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COMMENTS
| 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]
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REFERENCES
| A. H. Beiler, Recreations in the Theory of Numbers, page 91.
R. Honsberger, Mathematical Diamonds, MAA, 2003, see p. 79. [Added by N. J. A. Sloane, Jul 05 2009]
P. Ribenboim: The little book of big primes, Chapter on primes in arithmetic progression
H. Rademacher and O. Toeplitz, Von Zahlen und Figuren, Springer Verlag, Berlin, 1933, Zweite Auflage, see last chapter.
H. Rademacher & O. Toeplitz, The Enjoyment of Mathematics, pp. 187-192 Dover NY 1990.
J. E. Roberts, Lure of Integers, pp. 179-180 MAA 1992
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LINKS
| Bill Taylor, Posting to sci.math, Sep 13 1999
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FORMULA
| PrimeQ[ {k | GCD[ a[ n ], k ]=1; k= 2, ..., n-1} ] = True for all k.
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EXAMPLE
| 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}}}
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CROSSREFS
| The sequences consists of the n with A036997(n)=0.
Sequence in context: A074733 A001461 A173383 * A074964 A017822 A179042
Adjacent sequences: A048594 A048595 A048596 * A048598 A048599 A048600
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KEYWORD
| fini,full,nonn
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AUTHOR
| Labos E. (labos(AT)ana.sote.hu)
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EXTENSIONS
| Additional comments from Ulrich Schimke (ulrschimke(AT)aol.com), May 29 2001.
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