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A347008
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Numbers that can be written in exactly two ways as p*q+p+q where p and q are primes with p < q.
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1
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23, 47, 119, 167, 179, 323, 407, 419, 527, 587, 639, 647, 879, 935, 1043, 1103, 1119, 1139, 1215, 1223, 1247, 1271, 1331, 1367, 1403, 1455, 1595, 1599, 1631, 1691, 1775, 1791, 1859, 1895, 1931, 1943, 1959, 1967, 1979, 2099, 2111, 2175, 2183, 2219, 2231, 2435, 2471, 2483, 2495, 2543, 2559, 2603
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OFFSET
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1,1
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LINKS
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EXAMPLE
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a(3) = 119 is a term because 119 = 5*19+5+19 = 3*29+3+29 are the two ways to produce 119 = p*q+p+q with primes p < q.
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MAPLE
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N:= 10000: # to produce terms <= N
R:= Vector(N):
P:= select(isprime, [2, seq(i, i=3..N/3, 2)]):
for i from 1 to nops(P) do
for j from 1 to i-1 do
v:=P[i]*P[j]+P[i]+P[j];
if v <= N then R[v]:= R[v]+1 fi
od od:
select(t -> R[t]=2, [$1..N]);
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PROG
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(Python)
from sympy import primerange
from collections import Counter
def aupto(limit):
primes = list(primerange(2, limit//3+1))
nums = [p*q+p+q for i, p in enumerate(primes) for q in primes[i+1:]]
counts = Counter([k for k in nums if k <= limit])
return sorted(k for k in counts if counts[k] == 2)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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