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A269662 Semiprimes which are the sum of a twin prime pair plus one. 1
9, 25, 85, 121, 145, 205, 217, 301, 361, 481, 565, 697, 841, 865, 1141, 1285, 1717, 1765, 2041, 2101, 2305, 2461, 2581, 2605, 2641, 2965, 2977, 3241, 3337, 3397, 3865, 3901, 3997, 4285, 4537, 4681, 4765, 5317, 5377, 5461, 5941, 6001, 6241, 6505, 6937, 7081, 7117 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

LINKS

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

EXAMPLE

a(2) = 25 = 5 * 5 that is semiprime. Also, 25 = 11 + 13 + 1 where {11, 13} is a twin prime pair.

a(3) = 85 = 5 * 17 that is semiprime. Also, 55 = 41 + 43 + 1 where {41, 43} is a twin prime pair.

MATHEMATICA

A269662 = {}; Do[a = Prime[n]; b = a + 2; c = a + b + 1; If[PrimeQ[b] && PrimeOmega[c] == 2, AppendTo[A269662, c]], {n, 1000}]; A269662

Select[Range[1, 7200, 2], And[PrimeOmega@ # == 2, And[PrimeQ@ #, NextPrime[#] - 2] == # &[(# - 1)/2 - 1]] &] (* Michael De Vlieger, Apr 01 2016 *)

Select[1+Total[#]&/@Select[Partition[Prime[Range[500]], 2, 1], #[[2]]-#[[1]] == 2&], PrimeOmega[#]==2&] (* Harvey P. Dale, Apr 10 2016 *)

PROG

(PARI) for(n = 1, 1000, p=prime(n); q=p+2; s=p+q+1; if(isprime(q) && bigomega(s)==2, print1(s, ", ")));

(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, A054735, A118071.

Sequence in context: A141583 A147413 A066137 * A147428 A147436 A189118

Adjacent sequences:  A269659 A269660 A269661 * A269663 A269664 A269665

KEYWORD

nonn

AUTHOR

K. D. Bajpai, Mar 02 2016

STATUS

approved

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Last modified July 25 09:49 EDT 2021. Contains 346289 sequences. (Running on oeis4.)