1,2

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]

A. H. Beiler, Recreations in the Theory of Numbers, page 91.

H. Rademacher and O. Toeplitz, Von Zahlen und Figuren, Springer Verlag, Berlin, 1933, Zweite Auflage, see last chapter.

P. Ribenboim: The little book of big primes, Chapter on primes in arithmetic progression

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

Bill Taylor, Posting to sci.math, Sep 13 1999

PrimeQ[ {k | GCD[ a[ n ], k ]=1; k= 2, ..., n-1} ] = True for all k.

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}}}

The sequences consists of the n with A036997(n)=0.

Sequence in context: A107368 A074733 A001461 this_sequence A074964 A017822 A018465

Adjacent sequences: A048594 A048595 A048596 this_sequence A048598 A048599 A048600

fini,full,nonn

Labos E. (labos(AT)ana.sote.hu)

Additional comments from Ulrich Schimke (ulrschimke(AT)aol.com), May 29 2001.