A193165 Semiprimes m = p*q such that p-1 and q-1 are semiprimes.

25, 35, 49, 55, 77, 115, 121, 161, 235, 253, 295, 329, 413, 415, 517, 529, 535, 581, 649, 749, 835, 895, 913, 1081, 1135, 1169, 1177, 1253, 1315, 1357, 1589, 1735, 1795, 1837, 1841, 1909, 1915, 1969, 2209, 2335, 2395, 2429, 2461, 2497, 2513, 2515, 2681, 2773, 2815, 2893, 2935

Offset

1,1

Comments

Numbers of the form A005385(i)*A005385(j) for i,j >= 1. - Altug Alkan, Mar 22 2018

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

1969 is in the sequence because 1969 = 11*179, and 11-1 = 2*5 and 179-1 = 2*89 are semiprimes.

Maple

with(numtheory):for n from 2 to 3000 do: x:=factorset(n):y:=bigomega(n):z:=x[1]:zz:=n/z:if y=2 and type(z, prime)=true and type(zz, prime) = true and bigomega(z-1)=2 and bigomega(zz-1)=2 then printf(`%d, `, n): else fi:od:
# Alternate:
N:= 10000: # to get all terms <= N
P:= select(p -> isprime(p) and numtheory:-bigomega(p-1)=2, [$1..N/5]):
nP:= nops(P):
sort(select(`<=`, [seq(seq(P[i]*P[j], i=1..j), j=1..nP)], N)); # Robert Israel, Mar 23 2018

Mathematica

spsQ[n_]:=Module[{f=Transpose[FactorInteger[n]][[1]]}, PrimeOmega[n] == PrimeOmega[First[f]-1] == PrimeOmega[Last[f]-1]==2]; Select[Range[ 3000], spsQ] (* Harvey P. Dale, Jul 27 2011 *)

Prog

(PARI) upTo(lim)=my(u=List(), v=List(), t); forprime(p=2, lim\5, if(isprime(p\2), listput(u, p))); for(i=1, #u, for(j=1, i, t=u[i]*u[j]; if(t>lim, break, listput(v, t)))); vecsort(Vec(v)) \\ Charles R Greathouse IV, Jul 30 2011

Crossrefs

Subsequence of A001358.

Cf. A005385, A193227.

Sequence in context: A287918 A054550 A107472 * A060976 A036320 A339520

Adjacent sequences: A193162 A193163 A193164 * A193166 A193167 A193168

Keyword

nonn

Author

Michel Lagneau, Jul 17 2011

Status

approved