The On-Line Encyclopedia of Integer Sequences (OEIS)

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A264046

Numbers k such that k and k+6 are consecutive semiprimes.
(history; published version)

#10 by Harvey P. Dale at Sun Dec 24 16:25:19 EST 2023

STATUS

editing

approved

#9 by Harvey P. Dale at Sun Dec 24 16:25:16 EST 2023

MATHEMATICA

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

STATUS

approved

editing

#8 by Wesley Ivan Hurt at Thu Mar 09 15:09:18 EST 2023

STATUS

editing

approved

#7 by Wesley Ivan Hurt at Thu Mar 09 15:09:01 EST 2023

NAME

Numbers n k such that n k and nk+6 are consecutive semiprimes.

COMMENTS

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

EXAMPLE

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

STATUS

approved

editing

#6 by Bruno Berselli at Thu Nov 12 05:57:31 EST 2015

STATUS

proposed

approved

#5 by Charles R Greathouse IV at Mon Nov 02 15:49:34 EST 2015

STATUS

editing

proposed

#4 by Charles R Greathouse IV at Mon Nov 02 15:49:31 EST 2015

NAME

Numbers n such that n and n+k 6 are consecutive semiprimes, case k=6.

LINKS

Charles R Greathouse IV, <a href="/A264046/b264046.txt">Table of n, a(n) for n = 1..10000</a>

PROG

(PARI) 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

STATUS

proposed

editing

#3 by Zak Seidov at Mon Nov 02 07:07:57 EST 2015

STATUS

editing

proposed

#2 by Zak Seidov at Mon Nov 02 02:57:57 EST 2015

NAME

allocated for Zak SeidovNumbers n such that n and n+k are consecutive semiprimes, case k=6.

DATA

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

1,1

COMMENTS

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

EXAMPLE

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

CROSSREFS

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

KEYWORD

allocated

nonn

AUTHOR

Zak Seidov, Nov 02 2015

STATUS

approved

editing

#1 by Zak Seidov at Mon Nov 02 02:57:57 EST 2015

NAME

allocated for Zak Seidov

KEYWORD

allocated

STATUS

approved