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A133597
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Array of semiprimes, read by antidiagonals, where row k is the first of pairs of consecutive semiprimes j and j+k.
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0
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9, 4, 14, 6, 49, 21, 10, 22, 55, 25, 69, 51, 35, 91, 33, 15, 77, 58, 46, 119, 34, 26, 123, 106, 65, 62, 143, 38, 169, 39, 365, 161, 87, 74, 159, 57, 146, 437, 134, 371, 178, 111, 82, 183, 85, 237, 226, 458, 187, 505, 221, 129, 115, 185, 86
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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COMMENTS
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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.
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LINKS
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EXAMPLE
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The array begins:
==================================================================
n=......1....2.....3....4....5....6....7....8....9...10
==================================================================
k=1.|...9...14....21...25...33...34...38...57...85...86....A070552
k=2.|...4...49....55...91..119..143..159..183..185..203....A136196
k=3.|...6...22....35...46...62...74...82..115..155..166....A264043
k=4.|. 10...51....58...65...87..111..129..209..249..274....A264044
k=5.|..69...77...106..161..178..221..254..309..314..329....A264045
k=6.|..15..123...365..371..505..545..573..591..649..707....A264046
k=7.|..26...39...134..187..194..267..519..566..655..771....
k=8.|.169..437...458..614..723..737..905..965.1047.1059....
k=9.|.146..226...278..346.1018.1177.1273.1546.1594.1865....
k=10|.237..427..1027.1101.1661.2723.2747.3173.3295.3669....A217030
==================================================================
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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