id:A035096 - OEIS Search Results

Search: id:A035096

Displaying 1-1 of 1 results found.

page 1

a(n) = smallest number k such that p(n)*k+1 is prime, where p(n) is the n-th prime.

+0
5

1, 2, 2, 4, 2, 4, 6, 10, 2, 2, 10, 4, 2, 4, 6, 2, 12, 6, 4, 8, 4, 4, 2, 2, 4, 6, 6, 6, 10, 2, 4, 2, 6, 4, 8, 6, 10, 4, 14, 2, 2, 6, 2, 4, 18, 4, 10, 12, 24, 12, 2, 2, 6, 2, 6, 6, 8, 6, 4, 2, 6, 2, 4, 6, 6, 26, 6, 10, 6, 10, 14, 2, 6, 4, 12, 12, 24, 6, 8, 4, 2, 10, 2, 4, 10, 2, 8, 30 (list; graph; listen)

	OFFSET	`1,2`
	COMMENT	`These arithmetical progressions have prime differences. Note that both the terms of generated by this k values and the differences are primes as well.` `This is one possible generalization of "the least prime problem in special arithmetical progressions" when n in the nk+1 form is replaced by n-th prime number.` `Comment from Max Alekseyev, Jul 11 2008: Note that Dirichlet's theorem on primes in arithmetic progressions implies that a(n) always exists.`
	LINKS	`T. D. Noe, Table of n, a(n) for n=1..10000` `Eric Weisstein's World of Math, Dirichlet's theorem` `Index entries for sequences related to primes in arithmetic progressions`
	EXAMPLE	`a(15)=6 because in the p(15)k+1=47k+1 sequence the 6-th term is the first prime. It is 283.`
	CROSSREFS	`Analogous case is A034693.` `Sequence in context: A063789 A106264 A152423 this_sequence A066675 A097800 A083779` `Adjacent sequences: A035093 A035094 A035095 this_sequence A035097 A035098 A035099`
	KEYWORD	`nonn`
	AUTHOR	`Labos E. (labos(AT)ana.sote.hu)`

page 1

Search completed in 0.002 seconds

Last modified December 20 16:54 EST 2009. Contains 171081 sequences.

AT&T Labs Research