

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
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OFFSET

1,1


LINKS

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


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 62, 6 can be represented as 4+2 or 93 or 104, 9 can be represented as 145 or 156, but 10 cannot be represented by any such sum or difference as 4+1, 6+2, 9+3, 145, 156, 217, 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

Cf. A001358, A100493, A172096.
Sequence in context: A117847 A057990 A272779 * A091022 A133372 A100916
Adjacent sequences: A173474 A173475 A173476 * A173478 A173479 A173480


KEYWORD

nonn,easy


AUTHOR

JuriStepan Gerasimov, Nov 22 2010


EXTENSIONS

Corrected by D. S. McNeil, Nov 23 2010
Name clarified and Example section added by Antti Karttunen, Dec 20 2015


STATUS

approved



