

A256073


Numbers n representable as x*y + x + y, where x >= y > 1, such that all x's and y's in all representation(s) of n are primes.


2




OFFSET

1,1


COMMENTS

A subsequence of A254671.
From Robert Israel, May 27 2015: (Start)
n such that n+1 is not prime and not twice a prime, but every divisor of n+1 except for 1, 2, n+1 and (n+1)/2 is in A008864.
a(7) > 10^7 if it exists. (End)


LINKS

Table of n, a(n) for n = 1..6


EXAMPLE

23 = 5*3 + 5 + 3 = 7*2 + 7 + 2, and 2,3,5,7 are all primes, so 23 is a term.
71 = 11*5 + 11 + 5 = 17*3 + 17 + 3 = 23*2 + 23 + 2 = 7*8 + 8 + 7, but 8 is not a prime so 71 is not a term.
35 = 5*5 + 5 + 5 = 11*2 + 11 + 2 = 8*3 + 8 + 3, but 8 is not a prime so 35 is not a term.


MAPLE

filter:= proc(n)
local D;
D:= map(``, numtheory:divisors(n+1) minus {1, 2, n+1, (n+1)/2}, 1);
nops(D) >= 1 and andmap(isprime, D);
end proc:
select(filter, [$1..10^6]); # Robert Israel, May 27 2015


PROG

(Python)
import sympy
from sympy import isprime
TOP = 1000000
a = [0]*TOP
no= [0]*TOP
for y in xrange(2, TOP/2):
for x in xrange(y, TOP/2):
k = x*y + x + y
if k>=TOP: break
if no[k]==0:
a[k]=1
if not (isprime(x) and isprime(y)): no[k]=1
print [n for n in xrange(TOP) if a[n]>0 and no[n]==0]


CROSSREFS

Cf. A254671.
Sequence in context: A028394 A188199 A078117 * A032423 A063724 A317770
Adjacent sequences: A256070 A256071 A256072 * A256074 A256075 A256076


KEYWORD

nonn


AUTHOR

Alex Ratushnyak, Mar 14 2015


EXTENSIONS

More terms from Lars Blomberg, May 01 2015
Incorrect terms removed by Alex Ratushnyak, May 27 2015


STATUS

approved



