

A126636


Smallest odd prime q such that pq+2 is has exactly 3 prime factors (with multiplicity), where p is the nth odd prime.


2



41, 5, 37, 23, 13, 19, 17, 5, 5, 11, 7, 3, 11, 17, 17, 11, 7, 13, 5, 11, 7, 11, 11, 23, 5, 13, 11, 13, 11, 5, 5, 47, 17, 5, 3, 11, 7, 19, 5, 3, 13, 3, 7, 5, 19, 7, 31, 29, 7, 29, 7, 3, 11, 11, 11, 7, 7, 3, 3, 11, 5, 7, 3, 7, 5, 31, 13, 5, 7, 5, 11, 13, 7, 13, 11, 5, 19, 5, 7, 5, 3, 3, 7, 5, 3
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OFFSET

1,1


COMMENTS

Trieneprime (3primefactor) analog of A126610 (semiprimes) and A126608126609 (primes). This is the second row of the infinite array: A(k,n) = Smallest odd prime q such that pq+k has exactly 3 prime factors (with multiplicity), where p is the nth odd prime. The odd trieneprimes arising begin: 125, 27, 261, 255, 171, 325. The above A(k,n) is the 3rd plane of the infinite 3D array: A(j,k,n) = Smallest odd prime q such that pq+k has exactly j prime factors, where p is the nth odd prime.


LINKS

Table of n, a(n) for n=1..85.


FORMULA

a(n) = Min {q in A065091: q*A000040(n)+2 is in A014612}.


EXAMPLE

a(1) = 41 because oddprime(1)*1+2 = 3*41+2 = 125 = 5*5*5.
a(2) = 5 because oddprime(2)*5+2 = 5*5+2 = 27 = 3*3*3.
a(3) = 37 because oddprime(3)*37+2 = 7*37+2 = 261 = 3*3*29.
a(4) = 23 because oddprime(4)*3+2 = 11*23+2 = 255 = 3*5*17.
a(5) = 13 because oddprime(5)*13+2 = 13*13+2 = 171 = 3*3*19.
a(6) = 19 because oddprime(6)*19+2 = 17*19+2 = 325 = 5*5*13.


MAPLE

A001222 := proc(n) local ifcts, i ; ifcts := ifactors(n)[2] ; add(op(2, op(i, ifcts)), i=1..nops(ifcts)) ; end: isA014612 := proc(n) if A001222(n) = 3 then true ; else false ; fi ; end: A126636 := proc(n) local p, q; p := ithprime(n+1) ; q := 3 ; while not isA014612(p*q+2) do q := nextprime(q) ; od ; RETURN(q) ; end : for n from 1 to 100 do printf("%d, ", A126636(n)) ; od ; # R. J. Mathar, Feb 13 2007


CROSSREFS

Cf. A000040, A001358, A014612, A065091, A126608126609, A126610.
Sequence in context: A036189 A198190 A106424 * A095188 A215540 A107813
Adjacent sequences: A126633 A126634 A126635 * A126637 A126638 A126639


KEYWORD

easy,nonn


AUTHOR

Jonathan Vos Post, Feb 08 2007


EXTENSIONS

More terms from R. J. Mathar, Feb 13 2007


STATUS

approved



