A126636 Smallest odd prime q such that pq+2 is has exactly 3 prime factors (with multiplicity), where p is the n-th odd prime.

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

Offset

1,1

Comments

Trieneprime (3-prime-factor) analog of A126610 (semiprimes) and A126608-126609 (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 n-th 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 3-D array: A(j,k,n) = Smallest odd prime q such that pq+k has exactly j prime factors, where p is the n-th 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, A126608-126609, 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