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A326356
Lesser of twin primes p >= 5 for which phi(p+1)/phi(p-1) reaches record value, where phi(n) is the Euler totient function (A000010).
1
5, 2381, 3851, 20021, 50051, 52361, 424271, 470471, 602141, 2302301, 6806801, 16926911, 17497481, 69989921, 78278201, 183953771, 242662421, 468818351, 2156564411, 24912037151, 43874931101, 73769375681, 131104243271, 1360122864101, 1943064533411, 2635321709021, 3075260848661, 4078063299311
OFFSET
1,1
COMMENTS
Terms a(2)-a(23) were taken from the paper by Garcia et al.
Garcia et al. proved that assuming Dickson's conjecture, {phi(p+1)/phi(p-1) : p and p+2 are prime} is dense in [0, oo), and thus this sequence is infinite.
They give an example of a term p with 1099 digits with phi(p+1)/phi(p-1) = 3.11615...
What is the least value of lesser of twin primes p such that phi(p+1)/phi(p-1) > 2?
A candidate is p = 8183287190196092135163947564054981234789530779544672356881 for which the ratio is equal to 2.00047615... . - Giovanni Resta, Nov 01 2019
LINKS
EXAMPLE
The values of phi(p+1)/phi(p-1) for the first terms are 1 < 1.031... < 1.06 < 1.118... < 1.12 < ...
MATHEMATICA
s = {}; rm = 0; p = 5; Do[q = NextPrime[p]; If[q - p != 2, p = q; Continue[]]; r = EulerPhi[p + 1]/EulerPhi[p - 1]; If[r > rm, rm = r; AppendTo[s, p]]; p = q, {10^6}]; s
CROSSREFS
Except for 5, subsequence of A286715.
Sequence in context: A067944 A260843 A337551 * A200916 A346655 A114716
KEYWORD
nonn
AUTHOR
Amiram Eldar, Sep 11 2019
EXTENSIONS
a(24)-a(28) from Giovanni Resta, Nov 01 2019
STATUS
approved