A269663 Semiprimes which are the product of a twin prime pair minus one.

14, 34, 142, 898, 1762, 5182, 19042, 79522, 213442, 359998, 412162, 685582, 777922, 1192462, 1695202, 2585662, 4536898, 5143822, 5673922, 7225342, 12446782, 12659362, 12830722, 17040382, 17892898, 18818242, 20684302, 25100098, 32970562, 37601422, 46131262, 48441598

Offset

1,1

Comments

Subsequence of A103533 and A001358.

All the terms in this sequence, except a(1), are congruent to 1 (mod 3).

Links

K. D. Bajpai, Table of n, a(n) for n = 1..10000

Formula

a(n) = 2*A086870(n). - Ray Chandler, Apr 04 2016

Example

a(1) = 14 = 2 * 7 that is semiprime. Also, 3 * 5 - 1 = 14 where {3,5} is a twin prime pair.
a(2) = 34 = 2 * 17 that is semiprime. Also, 5 * 7 - 1 = 34 where {5,7} is a twin prime pair.

Maple

A269663:= proc() local a, b, d; a:= ithprime(n); b:=a+2; d:=(a*b)-1; if isprime(b)and bigomega(d)=2 then return (d): fi; end: seq(A269663 (n), n=1..1000);

Mathematica

A269663= {}; Do[a = Prime[n]; b = a + 2; c = a*b - 1; If[PrimeQ[b] && PrimeOmega[c] == 2, AppendTo[A269663, c]], {n, 1000}]; A269663
Select[Times @@ # - 1 & /@ Transpose@{#, 2 + #} &@ Select[Prime@ Range@ 900, NextPrime@ # == # + 2 &], PrimeOmega@ # == 2 &] (* Michael De Vlieger, Apr 01 2016 *)
Select[Times@@@Select[Partition[Prime[Range[1000]], 2, 1], #[[2]]-#[[1]]==2&]-1, PrimeOmega[ #]==2&] (* Harvey P. Dale, Mar 14 2023 *)

Prog

(PARI) for(n = 1, 1000, p = prime(n); q = p + 2; c=(p*q) - 1; if(isprime(q) && bigomega(c)==2, print1(c, ", ")));
(Magma) IsP2:=func< n | &+[k[2]: k in Factorization(n)] eq 2 >; [ s: n in [1..1000] | IsPrime(n) and IsPrime(n+2) and IsP2(s) where s is (n * (n+2) - 1)];

Crossrefs

Cf. A001097, A001358, A001359, A006512, A086870, A103533, A118071.

Sequence in context: A039449 A120875 A103533 * A046425 A018950 A159242

Adjacent sequences: A269660 A269661 A269662 * A269664 A269665 A269666

Keyword

nonn

Author

K. D. Bajpai, Mar 02 2016

Status

approved