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A057948 S-primes: let S={1,5,9, ... 4i+1, ...}; then an S-prime is in S but is not divisible by any members of S except itself and 1. 3
5, 9, 13, 17, 21, 29, 33, 37, 41, 49, 53, 57, 61, 69, 73, 77, 89, 93, 97, 101, 109, 113, 121, 129, 133, 137, 141, 149, 157, 161, 173, 177, 181, 193, 197, 201, 209, 213, 217, 229, 233, 237, 241, 249, 253, 257, 269, 277, 281, 293, 301, 309, 313, 317, 321, 329 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Factorization in S is not unique. See related sequences.

a(n) ~ C n log n / log log n, where C > 2. - Thomas Ordowski, Sep 09 2012

REFERENCES

T. M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, page 101, problem 1.

LINKS

Table of n, a(n) for n=0..55.

Eric Weisstein's World of Mathematics, Hilbert Number [From Eric W. Weisstein, Sep 15 2008]

EXAMPLE

21 is of the form 4i+1, but it is not divisible by any smaller S-primes, so 21 is in the sequence.

CROSSREFS

Cf. A054520, A057949, A057950.

Sequence in context: A016813 A198395 A190951 * A004958 A190887 A184479

Adjacent sequences:  A057945 A057946 A057947 * A057949 A057950 A057951

KEYWORD

nonn

AUTHOR

Jud McCranie, Oct 14 2000

STATUS

approved

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Last modified April 16 21:07 EDT 2014. Contains 240627 sequences.