[seqfan] Re: New Prime Curio about 199 by Post
Jonathan Post
jvospost3 at gmail.com
Tue Sep 15 00:25:56 CEST 2009
What would be a good way to submit this as a sequence or pair of seqs?
References:
In 1941, Molsen proved that for n equal to or greater than 199, the
interval n < p less than or equal to (8/7)n
always contains a prime of each of the forms 3x+1, 3x-1.
see Zhang, p.3
Generalizations of an Ancient Greek Inequality about the Sequence of Primes
Authors: Shaohua Zhang
(Submitted on 11 Sep 2009 (v1), last revised 12 Sep 2009 (this version, v2))
Abstract: In this note, we generalize an ancient Greek inequality
about the sequence of primes to the cases of arithmetic progressions
even multivariable polynomials with integral coefficients. We also
refine Bouniakowsky's conjecture...
K.Molsen, Zur Verallgemeinerung der Bertrandschen Postulates. Deutsche
Math. 6, 248-256, (1941).
n floor(8/7)n #primes 3x-1 #primes 3x+1 (in that interval n < p
less than or equal to (8/7)n)
199 227 1 2
200 228 1 2
201 229 1 3
202 230 1 3
203 232 1 3
204 233 2 3
205 234 2 3
206 235 2 3
207 236 2 3
208 237 2 3
209 238 2 3
210 240 3 3
211 241 3 4
Primes of form 3x-1 == A003627 = {2, 5, 11, 17, 23, 29, 41, 47, 53,
59, 71, 83, 89, 101, 107, 113, 131, 137, 149, 167, 173, 179, 191, 197,
227, 233, 239, 251, 257, 263, 269, 281, 293, 311, 317, 347, 353, 359,
383, 389, 401, 419, 431, 443, 449, 461, 467, 479, 491, 503, 509, 521,
557, 563, 569, 587, ...}
primes of form 3x+1 == A002476 = {7, 13, 19, 31, 37, 43, 61, 67, 73,
79, 97, 103, 109, 127, 139, 151, 157, 163, 181, 193, 199, 211, 223,
229, 241, 271, 277, 283, 307, 313, 331, 337, 349, 367, 373, 379, 397,
409, 421, 433, 439, 457, 463, 487, 499, 523, 541, 547, 571, 577, 601,
607, 613, 619, ...}
Thank you,
Jonathan Vos Post
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