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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 MATHEMATICA sol[t_] := Solve[x >= y > 1 && x y + x + y == t, {x, y}, Integers]; Select[Range[100], AllTrue[Flatten[{x, y} /. sol[#]], PrimeQ]&] (* Jean-François Alcover, Jul 28 2020 *) PROG (Python) import sympy from sympy import isprime TOP = 10000 a = [0]*TOP no= [0]*TOP for y in range(2, TOP//2): for x in range(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 range(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 April 24 15:42 EDT 2024. Contains 371960 sequences. (Running on oeis4.)