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A173477
Semiprimes having no representation of the form semiprime(n)-+n, where semiprime(n) = A001358(n).
1
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
OFFSET
1,1
LINKS
EXAMPLE
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.
MAPLE
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
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
Corrected by D. S. McNeil, Nov 23 2010
Name clarified and Example section added by Antti Karttunen, Dec 20 2015
STATUS
approved