A155764 Records in A047160.

0, 1, 3, 9, 15, 18, 21, 27, 33, 39, 42, 45, 48, 75, 87, 93, 117, 120, 135, 138, 168, 183, 210, 228, 300, 333, 369, 393, 453, 525, 621, 720, 810, 846, 1086, 1281, 1305, 1515, 1590, 1617, 1722, 1794, 1833, 1851, 2010, 2064, 2085, 2112, 2217, 2352, 2754, 2784

Offset: 1

Author

T. D. Noe, Jan 27 2009

Keywords

• nonn

Comments

Other than a(2)=1, every known term is a multiple of three. Equivalently, assuming A155765(n) - a(n) != 3, no term of A155765 is a multiple of three. - Jason Kimberley, Oct 24 2012

Conjecture 1: a(n) < 0.138*log(A155765(n))^3.6 for n > 4. Conjecture 2: If Conjecture 1 and Goldbach's conjecture hold, for any integer m > 22, there exist at least one pairs of primes m-d and m+d such that d < 0.138*log(m)^3.6. - Ya-Ping Lu, Nov 27 2020

Links

• Gilmar Rodriguez Pierluissi, Table of n, a(n) for n = 1..64 (terms 1..61 from T. D. Noe)
• OEIS (Plot 2), Plot of (log(A155765(n)), log(A155764(n))) - _Jason Kimberley_, Oct 24 2012

Crossrefs

Cf. A155765 (where records occur in A047160).

Programs

Mathematica

mgppp[n_?EvenQ]/;n>3:=Block[{m=PrimePi[n/2],p},While[!PrimeQ[n-(p=Prime[m])],m--];p];
dist[n_?EvenQ]:=Module[{d},{m=n/2,d=(m-mgppp[n])};d]
For[n=4;a=-1,True,n+=2,b=dist[n];If[b>a,Print[b];a=b]]
(* Gilmar Rodriguez Pierluissi, Aug 27 2018 *)

Python

from sympy import isprime
a_rec = -1
m = 2
while 1:
    a = 0
    while a < m - 1:
        if isprime(m-a) == 1 and isprime(m+a) == 1:
            if a > a_rec:
                print(a)
                a_rec = a
            break
        a += 1
m += 1 # Ya-Ping Lu, Nov 27 2020

Formula

a(n) = A047160(A155765(n)). - Jason Kimberley, Sep 01 2011