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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
8, 11, 15, 17, 23, 31 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 20 12:47 EDT 2019. Contains 328257 sequences. (Running on oeis4.)