

A123255


Numbers k such that 4k+1, 4k+2, and 4k+3 are all semiprimes.


1



8, 21, 23, 30, 35, 50, 53, 54, 75, 98, 111, 158, 174, 210, 230, 260, 284, 315, 336, 350, 410, 440, 459, 473, 485, 495, 525, 545, 554, 576, 590, 608, 615, 629, 660, 680, 683, 774, 846, 900, 923, 966, 975, 989, 1071
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

4k+4 = 4*(k+1) = 2*2*(k+1) cannot be semiprime as well, as it has at least 3 prime factors with multiplicity. Thus there are no four consecutive semiprimes.


LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..1000


FORMULA

{k: 4k+1 is in A001358 AND 4k+2 is in A001358 AND 4k+3 is in A001358}. {k: 4k+1 is in A070552 AND 4k+2 is in A070552}. {(A056809(i)1)/4}.


EXAMPLE

a(1) = 8 because 4*8+1 = 33 = 3*11 is semiprime and 4*8+2 = 34 = 2*17 is semiprime and 4*8+3 = 35 = 3*5 is semiprime.


MATHEMATICA

Select[Range[1100], Union[PrimeOmega[4#+{1, 2, 3}]]=={2}&] (* Harvey P. Dale, Feb 02 2015 *)


PROG

(MAGMA) IsSemiprime:=func< n  &+[k[2]: k in Factorization(n)] eq 2 >; [ n: n in [2..1500]  IsSemiprime(4*n+1) and IsSemiprime(4*n+2) and IsSemiprime(4*n+3) ]; // Vincenzo Librandi, Dec 22 2010


CROSSREFS

Cf. A001358, A056809, A070552.
Sequence in context: A130021 A003864 A182602 * A053750 A321439 A271921
Adjacent sequences: A123252 A123253 A123254 * A123256 A123257 A123258


KEYWORD

easy,nonn


AUTHOR

Jonathan Vos Post, Oct 09 2006


EXTENSIONS

336 and 680 added by Vincenzo Librandi, Dec 22 2010


STATUS

approved



