OFFSET
1,2
COMMENTS
1 is in the sequence by convention.
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
Benoit Cloitre, Plot of a(n)/A274212(n)
FORMULA
Arithmetic conjecture: the equation a(n+1) - a(n) = 2r has infinitely many solutions for any fixed integer value r >= 1.
Analytic conjecture: a(n) is asymptotic to D*n*log(n)^2 for a constant D > 0.4 hence lim_{n->oo} a(n)/A274212(n) exists (see link).
EXAMPLE
65 = 5*13 is a term because there are twin prime pairs (3,5) and (11,13).
MAPLE
N:= 10^4: # to get all terms <= N
Primes:= select(isprime, {seq(i, i=3..N, 2)}):
Twins:= Primes intersect map(`+`, Primes, 2):
S:= {1}:
for p in Twins do
S:= map(s -> seq(s*p^i, i=0..ilog[p](floor(N/s))), S)
od:
sort(convert(S, list)); # Robert Israel, Jun 15 2016
MATHEMATICA
Join[{1}, Select[Range[1, 1000, 2], AllTrue[FactorInteger[#][[All, 1]], PrimeQ[# - 2]& ]& ] ] (* Jean-François Alcover, Jun 16 2016 *)
PROG
(PARI) for(n=1, 1000, if(prod(i=1, omega(n), isprime(factor(n)[i, 1]-2))==1, print1(n, ", ")))
CROSSREFS
KEYWORD
nonn
AUTHOR
Benoit Cloitre, Jun 15 2016
STATUS
approved