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
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
KEYWORD
nonn
AUTHOR
T. D. Noe, Jan 27 2009
STATUS
approved