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A173477
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Semiprimes having no representation of the form semiprime(n)-+n, where semiprime(n) = A001358(n).
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1
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10, 15, 25, 26, 35, 38, 39, 58, 65, 82, 85, 87, 91, 94, 118, 119, 121, 123, 133, 134, 142, 143, 155, 166, 183, 185, 201, 202, 209, 213, 217, 226, 237, 253, 267, 274, 278, 287, 295, 298, 299, 301, 303, 305, 314, 319, 321, 339, 355, 362, 371, 377, 381, 395, 407, 413, 415, 417, 422, 427
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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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Listing the first eight terms of A001358 gives us:
n: 1, 2, 3, 4, 5, 6, 7, 8, ...
4, 6, 9, 10, 14, 15, 21, 22, ...
We see that 4 can be represented as 6-2, 6 can be represented as 4+2 or 9-3 or 10-4, 9 can be represented as 14-5 or 15-6, but 10 cannot be represented by any such sum or difference as 4+1, 6+2, 9+3, 14-5, 15-6, 21-7, and also any difference A001358(n)-n after that will miss it. Thus 10 is the first semiprime included in this sequence.
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MAPLE
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N:= 2000: # to use semiprimes <= N
Primes:= select(isprime, [2, seq(i, i=3..N, 2)]):
Semiprimes:= select(`<=`, {seq(seq(Primes[i]*Primes[j], i=1..j), j=1..nops(Primes))}, N):
sort(convert(Semiprimes minus {seq}(i+Semiprimes[i], i=1..nops(Semiprimes)) minus {seq}(Semiprimes[i]-i, i=1..nops(Semiprimes))), list)); # Robert Israel, Dec 20 2015
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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