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%I #7 Jul 11 2015 16:57:49
%S 3,3,3,5,5,5,3,3,3,3,5,3,3,3,5,5,3,3,3,3,5,3,3,5,5,5,3,3,5,13,3,3,3,3,
%T 13,5,3,3,3,3,3,3,3,3,3,3,5,7,13,7,7,13,7,5,3,5,3,7,3,3,5,3,3,7,3,5,5,
%U 3,3,5,13,3,3,13,5,3,3,5,3,3,5,7,13,41,71,41,13,7,5,3,3,11,3,3,3,5,3,7,7
%N Array read by antidiagonals: A(i,j) = smallest odd prime r such that pqr+2 is prime, where p is the i-th odd prime and q is the j-th odd prime.
%C Two-dimensional analog of 1-dimensional semiprime-derived A126608.
%F A(i,j) = Min{r in A065091 such that A065091(i)*A065091(j)*r+2 is in A000040}. A(i,j) = Min{r in A065091 such that A065091(i)*A065091(j)*r+2 is in A065091}.
%F A(i,j)=A(j,i); i,j=1,2,3,... - _R. J. Mathar_, Feb 13 2007
%e A(1,1) = 3 because oddprime(1)*oddprime(1)*3+2 = 3*3*3+2 = 29 is prime.
%e A(2,3) = 3 because oddprime(2)*oddprime(3)*3+2 = 5*7*3+2 = 107 is prime.
%e A(2,7) = 13 because oddprime(2)*oddprime(7)*31+2 = 5*19*13+2 = 1237 is prime.
%e A(5,6) = 7 because oddprime(4)*oddprime(5)*7+2 = 13*17*7+2 = 1549 is prime.
%e A(6,8) = 41 because oddprime(6)*oddprime(8)*41+2 = 17*23*41+2 = 16033 is prime.
%e A(7,7) = 71 because oddprime(7)*oddprime(7)*71+2 = 19*19*71+2 = 25633 is prime.
%e Array begins
%e i\j...1....2....3....4....5....6....7....8....9....10
%e .1|...3....3....5....3....5....5....3....5....3....3....5....5....3...11.
%e .2|...3....5....3....3....3....3...13....3....5....3....3....3....3...23.
%e .3|...5....3....3....3....5....3....3....7....7....3....5....3...11...43.
%e .4|...3....3....3....5....3....3...13....3....5....7....3...17....7....3.
%e .5|...5....3....5....3....3....7....3...13...13....5...17....3....5...61.
%e .6|...5....3....3....3....7....5....3...41....3....3....3...11....7....3.
%e .7|...3...13....3...13....3....3...71....7...37...11....3....3...23...67.
%e .8|...5....3....7....3...13...41....7....5....3....3...37...17....3....5.
%e .9|...3....5....7....5...13....3...37....3...29....3....3...29....7....3.
%e 10|...3....3....3....7....5....3...11....3....3...17....5...19....3....3.
%e 11|...5....3....5....3...17....3....3...37....3....5...11...37...29...43.
%e 12|...5....3....3...17....3...11....3...17...29...19...37...11....7....3.
%e 13|...3....3...11....7....5....7...23....3....7....3...29....7...11....7.
%e 14|..11...23...43....3...61....3...67....5....3....3...43....3....7....5.
%p A126661 := proc(i,j) local p,q,r ; p := ithprime(i+1) ; q := ithprime(j+1) ; r := 3 ; while not isprime(p*q*r+2) do r := nextprime(r) ; od ; RETURN(r) ; end ; ijmax := 14 ; for d from 1 to ijmax do for i from 1 to d do printf("%d, ",A126661(i,d-i+1)) ; od ; od : # _R. J. Mathar_, Feb 13 2007
%Y Cf. A000040, A126608-A126609, A126660.
%K easy,tabl,nonn
%O 1,1
%A _Jonathan Vos Post_, Feb 10 2007
%E Edited by _R. J. Mathar_, Feb 13 2007
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