A374694 Primes that occur more than once in A373464.
8231, 10289, 10499, 15551, 20249, 40499, 49391, 51449, 59581, 96667, 117911, 123479, 152249, 159013, 161999, 165887, 239999, 255551, 257249, 260999, 288077, 292667, 314927, 319439, 453961, 514499, 519089, 524287, 524789, 530711, 565247, 580607, 657017, 774143
Offset: 1
Keywords
Examples
8231 is a term since (2, 41, 587, 8231) and (647, 1511, 3527, 8231) are quadruples of primes and (2+1, 41+1, 587+1, 8231+1) and (647+1, 1511+1, 3527+1, 8231+1) are geometric progressions. 10289 is a term since (239, 839, 2939, 10289) and (809, 1889, 4409, 10289) are quadruples of primes and (239+1, 839+1, 2939+1, 10289+1) and (809+1, 1889+1, 4409+1, 10289+1) are geometric progressions.
Links
- Chai Wah Wu, Table of n, a(n) for n = 1..192
Crossrefs
Cf. A373464.
Programs
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Python
from itertools import islice from fractions import Fraction from sympy import nextprime def A374694_gen(): # generator of terms p, plist, pset = 1, [], set() while True: p = nextprime(p) flag = False for q in plist: r = Fraction(q+1,p+1) q2 = r*(q+1)-1 if q2 < 2: break if q2.denominator == 1: q2 = int(q2) if q2 in pset: q3 = r*(q2+1)-1 if q3 < 2: break if q3.denominator == 1 and int(q3) in pset: if flag: yield p break flag = True plist = [p]+plist pset.add(p) A374694_list = list(islice(A374694_gen(),20))
Comments