editing

approved

Cf. A014612, A072966.

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editing

editing

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3-almost prime analogue analog of A072966, numbers which are not the sum of two semiprimes. In general, it seems that almost all even numbers can be written as the sum of two k-almost primes for any positive integer k. - T. D. Noe, Nov 06 2006

nn=10000; t3=Select[Range[2, nn], Plus@@Last/@FactorInteger[ # ]==3&]; t3sum=Table[0, {nn}]; Do[n=t3[[i]]+t3[[j]]; If[n<=nn, t3sum[[n]]=1], {i, Length[t3]}, {j, i, Length[t3]}]; Flatten[Position[t3sum, 0]] - _(* _T. D. Noe_, Nov 06 2006 *)

approved

editing

_Jonathan Vos Post (jvospost3(AT)gmail.com), _, Sep 27 2006

3-almost prime analogue of A072966, numbers which are not the sum of two semiprimes. In general, it seems that almost all even numbers can be written as the sum of two k-almost primes for any positive integer k. - _T. D. Noe (noe(AT)sspectra.com), _, Nov 06 2006

nn=10000; t3=Select[Range[2, nn], Plus@@Last/@FactorInteger[ # ]==3&]; t3sum=Table[0, {nn}]; Do[n=t3[[i]]+t3[[j]]; If[n<=nn, t3sum[[n]]=1], {i, Length[t3]}, {j, i, Length[t3]}]; Flatten[Position[t3sum, 0]] - _T. D. Noe (noe(AT)sspectra.com), _, Nov 06 2006

Edited by _T. D. Noe (noe(AT)sspectra.com), _, Nov 06 2006

easy,fini,full,nonn,new

Jonathan Vos Post (jvospost2jvospost3(AT)yahoogmail.com), Sep 27 2006

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, 85, 99, 101, 109, 163

1,32

3-almost prime analogue of A072966 Numbers , 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 even 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, . T. D. are 0Noe (noe(?AT), 13, 38, etceterasspectra.com), Nov 06 2006

nn=10000; t3=Select[Range[2, nn], Plus@@Last/@FactorInteger[ # ]==3&]; t3sum=Table[0, {nn}]; Do[n=t3[[i]]+t3[[j]]; If[n<=nn, t3sum[[n]]=1], {i, Length[t3]}, {j, i, Length[t3]}]; Flatten[Position[t3sum, 0]] - T. D. Noe (noe(AT)sspectra.com), Nov 06 2006

easy,fini,full,nonn,new

Edited by T. D. Noe (noe(AT)sspectra.com), Nov 06 2006

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

1,3

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.

Complement of Sumset {A014612} + {A014612}.

Cf. A014612.

easy,fini,full,nonn,new

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

approved