

A241817


Semiprimes sp such that sp3 is prime.


2



6, 10, 14, 22, 26, 34, 46, 62, 74, 82, 86, 106, 134, 142, 166, 194, 202, 214, 226, 254, 274, 314, 334, 362, 382, 386, 422, 446, 466, 482, 502, 526, 566, 622, 634, 662, 694, 746, 842, 862, 866, 886, 914, 922, 974, 1042, 1094, 1126, 1154, 1174, 1226, 1234, 1262
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OFFSET

1,1


COMMENTS

Even numbers of the form 2p, p prime, that can be expressed as the sum of two primes in at least two ways as 2p = p + p = 3 + (2p3). For example, 34 is in the sequence because 34 = 2*17 = 17 + 17 = 3 + 31. These are the only numbers that have Goldbach partitions with both a minimum and a maximum possible difference between their prime parts, i.e., pp = 0 and (2p3)3 = 2p6 respectively.  Wesley Ivan Hurt, Apr 08 2018


LINKS

K. D. Bajpai, Table of n, a(n) for n = 1..2500


FORMULA

a(n) = 2 * A063908(n).  Wesley Ivan Hurt, Apr 08 2018


EXAMPLE

a(2) = 10 = 2*5, which is semiprime and 103 = 7 is a prime.
a(6) = 34 = 2*17, which is semiprime and 343 = 31 is a prime.


MAPLE

with(numtheory): A241817:= proc(); if bigomega(x)=2 and isprime(x3) then RETURN (x); fi; end: seq(A241817 (), x=1..3000);


MATHEMATICA

2 Select [Prime[Range[5!]], PrimeQ[2 #  3] &] (* Vincenzo Librandi, Apr 10 2018 *)
Select[Range[1500], PrimeOmega[#]==2&&PrimeQ[#3]&] (* Harvey P. Dale, Oct 14 2018 *)


CROSSREFS

Cf. A001358, A063908, A092207, A123017, A198327.
Sequence in context: A119431 A207574 A278972 * A181628 A023387 A315236
Adjacent sequences: A241814 A241815 A241816 * A241818 A241819 A241820


KEYWORD

nonn


AUTHOR

K. D. Bajpai, Apr 29 2014


STATUS

approved



