A264045 -id:A264045 - cp's OEIS frontend

A264046 Numbers k such that k and k+6 are consecutive semiprimes.

15, 123, 365, 371, 505, 545, 573, 591, 649, 707, 807, 843, 943, 1067, 1159, 1247, 1357, 1405, 1529, 1555, 1633, 1739, 1745, 1829, 1843, 1897, 1909, 1985, 2149, 2159, 2209, 2285, 2329, 2353, 2363, 2407, 2413, 2463, 2501, 2643, 2773, 2779

Offset: 1

Zak Seidov, Nov 02 2015

nonn

Note that a(1) = 15 = A131109(k=6).

			15 = A001358(6) and 21 = A001358(7).

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Cf. A001358, A065516, A123375, A131109, A136196, A264043, A264044, A264045.

Select[Partition[Select[Range[3000],PrimeOmega[#]==2&],2,1],#[[2]]-#[[1]]==6&][[;;,1]] (* Harvey P. Dale, Dec 24 2023 *)

is(n)=if(bigomega(n)!=2 || bigomega(n+6)!=2, return(0)); for(i=1,5,if(bigomega(n+i)==2, return(0))); 1 \\ Charles R Greathouse IV, Nov 02 2015

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

Original entry on oeis.org

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

Offset: 1

Jonathan Vos Post, Dec 27 2007

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.

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

Cf. A001358, A070552, A136196.

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 *)

Corrected and edited by Giovanni Resta, Jun 20 2016

cp's OEIS Frontend

A264046 Numbers k such that k and k+6 are consecutive semiprimes.

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