The On-Line Encyclopedia of Integer Sequences (OEIS)

A123093 revision #1

A123093

Numbers which are not the sum of two 3-almost primes.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 21, 22, 23, 25, 27, 29, 31, 33, 34, 37, 41, 43, 44, 49, 51, 59, 61, 66, 67

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OFFSET

1,3

COMMENTS

3-almost prime analogue of A072966 Numbers which are not the sum of two semiprimes. Once we see that the 7 consecutive numbers 68, 69, 70, 71, 72, 73, 74 can be written as the sum of two 3-almost primes, we have all graeter integers covered, since multiples of A014612(1) = 8 can be added freely. In general, it seems that almost all numbers can be written as the sum of two k-almost primes for any positive integer k. The open problem is k = 2 (Goldbach's conjecture). The number of nonnegative numbers which are not the sum of two n-almost primes for n = 1, 2, 3, ... are 0(?), 13, 38, etcetera.

LINKS

Table of n, a(n) for n=1..38.

FORMULA

Complement of Sumset {A014612} + {A014612}.

CROSSREFS

Cf. A014612.

Sequence in context: A337379 A121684 A191853 * * A191932 A044920

Adjacent sequences: A123090 A123091 A123092 * A123094 A123095 A123096

KEYWORD

easy,fini,full,nonn,new

AUTHOR

Jonathan Vos Post (jvospost2(AT)yahoo.com), Sep 27 2006

STATUS

approved