

A109383


5almost primes of the form semiprime + 1.


5



112, 120, 162, 300, 304, 378, 392, 396, 408, 520, 552, 567, 592, 612, 630, 656, 675, 680, 688, 696, 700, 750, 780, 918, 924, 944, 952, 980, 990, 1044, 1100, 1116, 1136, 1140, 1160, 1168, 1170, 1242, 1264, 1272, 1300, 1323, 1352, 1372, 1380, 1386, 1416, 1470
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OFFSET

1,1


LINKS

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


FORMULA

a(n) is in this sequence iff a(n) is in A014614 and (a(n)1) is in A001358.


EXAMPLE

a(1) = 112 because (3*37)+1 = (2^4) * 7 = 112.
a(2) = 120 because (7*17)+1 = (2^3) * 3 * 5 = 120.
a(3) = 162 because (7*23)+1 = 2 * (3^4) = 162.


MATHEMATICA

f[n_] := Plus @@ Last /@ FactorInteger[n]; Select[Range[1500], f[ # ] == 5 && f[ #  1] == 2 &] (* Ray Chandler, Mar 20 2007 *)


PROG

(PARI) v=vector(10000); i=0; for(n=1, 9e99, if(issemi(n)&bigomega(n+1)==5, v[i++]=n+1; if(i==#v, return))); v \\ Charles R Greathouse IV, Feb 14 2011


CROSSREFS

Primes are in A000040. Semiprimes are in A001358. 5almost primes are in A014614.
Primes of the form semiprime + 1 are in A005385 (safe primes).
Semiprimes of the form semiprime + 1 are in A109373.
3almost primes of the form semiprime + 1 are in A109067.
4almost primes of the form semiprime + 1 are in A109287.
5almost primes of the form semiprime + 1 are in this sequence.
Least nalmost prime of the form semiprime + 1 are in A128665.
Cf. A077065, A079148, A092307.
Sequence in context: A300006 A262521 A096680 * A281926 A036301 A117723
Adjacent sequences: A109380 A109381 A109382 * A109384 A109385 A109386


KEYWORD

easy,nonn,changed


AUTHOR

Jonathan Vos Post, Aug 25 2005


EXTENSIONS

Extended by Ray Chandler, Mar 20 2007


STATUS

approved



