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

1,3

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 16 and 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

Formula

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

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 *)

Prog

(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

Crossrefs

Cf. A155765 (where records occur in A047160).

Sequence in context: A310328 A043381 A100331 * A259754 A277569 A310329

Adjacent sequences: A155761 A155762 A155763 * A155765 A155766 A155767

Keyword

nonn

Author

T. D. Noe, Jan 27 2009

Status

approved