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%I #10 Jun 20 2016 05:14:38
%S 9,4,14,6,49,21,10,22,55,25,69,51,35,91,33,15,77,58,46,119,34,26,123,
%T 106,65,62,143,38,169,39,365,161,87,74,159,57,146,437,134,371,178,111,
%U 82,183,85,237,226,458,187,505,221,129,115,185,86
%N Array of semiprimes, read by antidiagonals, where row k is the first of pairs of consecutive semiprimes j and j+k.
%C Every semiprime occurs in this table exactly once. Note that similar tables exist for k-almost primes (integers with exactly k prime factors, with multiplicity), this being the k=2 slice of a 3-dimensional array.
%e The array begins:
%e ==================================================================
%e n=......1....2.....3....4....5....6....7....8....9...10
%e ==================================================================
%e k=1.|...9...14....21...25...33...34...38...57...85...86....A070552
%e k=2.|...4...49....55...91..119..143..159..183..185..203....A136196
%e k=3.|...6...22....35...46...62...74...82..115..155..166....A264043
%e k=4.|. 10...51....58...65...87..111..129..209..249..274....A264044
%e k=5.|..69...77...106..161..178..221..254..309..314..329....A264045
%e k=6.|..15..123...365..371..505..545..573..591..649..707....A264046
%e k=7.|..26...39...134..187..194..267..519..566..655..771....
%e k=8.|.169..437...458..614..723..737..905..965.1047.1059....
%e k=9.|.146..226...278..346.1018.1177.1273.1546.1594.1865....
%e k=10|.237..427..1027.1101.1661.2723.2747.3173.3295.3669....A217030
%e ==================================================================
%t v = Select[Range[5000], PrimeOmega[#]==2 &]; L[k_] := L[k] = v[[Select[Range[Length[v]-1], v[[#+1]] - v[[#]] == k &]]]; Flatten@ Table[ Table[L[k-j+1][[j]], {j, k}], {k, 10}] (* _Giovanni Resta_, Jun 20 2016 *)
%Y Cf. A001358, A070552, A136196.
%K easy,nonn,tabl
%O 1,1
%A _Jonathan Vos Post_, Dec 27 2007
%E Corrected and edited by _Giovanni Resta_, Jun 20 2016
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