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A269663 Semiprimes which are the product of a twin prime pair minus one. 2
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 (list; graph; refs; listen; history; text; internal format)
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 *)

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) (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

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Last modified August 1 17:43 EDT 2021. Contains 346402 sequences. (Running on oeis4.)