

A264045


Numbers n such that n and n+5 are consecutive semiprimes.


3



69, 77, 106, 161, 178, 221, 254, 309, 314, 329, 341, 386, 398, 417, 422, 473, 554, 662, 674, 689, 758, 794, 934, 974, 998, 1094, 1121, 1149, 1169, 1214, 1294, 1502, 1517, 1522, 1541, 1569, 1673
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

Note that a(1)=69=A131109(k=5).


LINKS

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


FORMULA

a(n) >> n log n.  Charles R Greathouse IV, Nov 02 2015


EXAMPLE

a(1)=69=A001358(24) and a(1)+k=74=A001358(25).


MATHEMATICA

Flatten[Position[Partition[Table[If[PrimeOmega[n]==2, 1, 0], {n, 2000}], 6, 1], _?(#=={1, 0, 0, 0, 0, 1}&)]] (* Harvey P. Dale, Dec 16 2015 *)


PROG

(PARI) is(n)=if(n%4==1, isprime((n+5)/2) && bigomega(n)==2, n%4==2 && isprime(n/2) && bigomega(n+5)==2) && bigomega(n+1)!=2 && bigomega(n+2)!=2 && bigomega(n+3)!=2 && bigomega(n+4)!=2 \\ Charles R Greathouse IV, Nov 02 2015


CROSSREFS

Cf. A001358, A065516, A123375, A131109, A136196, A264043, A264044.
Sequence in context: A325386 A260428 A168477 * A295806 A210614 A235226
Adjacent sequences: A264042 A264043 A264044 * A264046 A264047 A264048


KEYWORD

nonn


AUTHOR

Zak Seidov, Nov 02 2015


STATUS

approved



