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A133597 Array of semiprimes, read by antidiagonals, where row k is the first of pairs of consecutive semiprimes j and j+k. 0
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)
OFFSET

1,1

COMMENTS

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.

LINKS

Table of n, a(n) for n=1..55.

EXAMPLE

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

==================================================================

MATHEMATICA

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 *)

CROSSREFS

Cf. A001358, A070552, A136196.

Sequence in context: A153698 A168203 A248310 * A075066 A061363 A100077

Adjacent sequences:  A133594 A133595 A133596 * A133598 A133599 A133600

KEYWORD

easy,nonn,tabl

AUTHOR

Jonathan Vos Post, Dec 27 2007

EXTENSIONS

Corrected and edited by Giovanni Resta, Jun 20 2016

STATUS

approved

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Last modified October 23 17:32 EDT 2019. Contains 328373 sequences. (Running on oeis4.)