A173477 Semiprimes having no representation of the form semiprime(n)-+n, where semiprime(n) = A001358(n).

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

Author

Juri-Stepan Gerasimov, Nov 22 2010

Keywords

• nonn
• easy

Examples

			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.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001358, A100493, A172096.

Programs

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

Extensions

Corrected by D. S. McNeil, Nov 23 2010

Name clarified and Example section added by Antti Karttunen, Dec 20 2015