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A126661
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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.
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3
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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, 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, 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
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OFFSET
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1,1
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COMMENTS
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Two-dimensional analog of 1-dimensional semiprime-derived A126608.
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LINKS
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Table of n, a(n) for n=1..99.
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FORMULA
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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}.
A(i,j)=A(j,i); i,j=1,2,3,... - R. J. Mathar, Feb 13 2007
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EXAMPLE
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A(1,1) = 3 because oddprime(1)*oddprime(1)*3+2 = 3*3*3+2 = 29 is prime.
A(2,3) = 3 because oddprime(2)*oddprime(3)*3+2 = 5*7*3+2 = 107 is prime.
A(2,7) = 13 because oddprime(2)*oddprime(7)*31+2 = 5*19*13+2 = 1237 is prime.
A(5,6) = 7 because oddprime(4)*oddprime(5)*7+2 = 13*17*7+2 = 1549 is prime.
A(6,8) = 41 because oddprime(6)*oddprime(8)*41+2 = 17*23*41+2 = 16033 is prime.
A(7,7) = 71 because oddprime(7)*oddprime(7)*71+2 = 19*19*71+2 = 25633 is prime.
Array begins
i\j...1....2....3....4....5....6....7....8....9....10
.1|...3....3....5....3....5....5....3....5....3....3....5....5....3...11.
.2|...3....5....3....3....3....3...13....3....5....3....3....3....3...23.
.3|...5....3....3....3....5....3....3....7....7....3....5....3...11...43.
.4|...3....3....3....5....3....3...13....3....5....7....3...17....7....3.
.5|...5....3....5....3....3....7....3...13...13....5...17....3....5...61.
.6|...5....3....3....3....7....5....3...41....3....3....3...11....7....3.
.7|...3...13....3...13....3....3...71....7...37...11....3....3...23...67.
.8|...5....3....7....3...13...41....7....5....3....3...37...17....3....5.
.9|...3....5....7....5...13....3...37....3...29....3....3...29....7....3.
10|...3....3....3....7....5....3...11....3....3...17....5...19....3....3.
11|...5....3....5....3...17....3....3...37....3....5...11...37...29...43.
12|...5....3....3...17....3...11....3...17...29...19...37...11....7....3.
13|...3....3...11....7....5....7...23....3....7....3...29....7...11....7.
14|..11...23...43....3...61....3...67....5....3....3...43....3....7....5.
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MAPLE
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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
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CROSSREFS
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Cf. A000040, A126608-A126609, A126660.
Sequence in context: A192451 A129856 A136800 * A162226 A001650 A130175
Adjacent sequences: A126658 A126659 A126660 * A126662 A126663 A126664
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KEYWORD
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easy,tabl,nonn
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AUTHOR
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Jonathan Vos Post, Feb 10 2007
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EXTENSIONS
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Edited by R. J. Mathar, Feb 13 2007
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STATUS
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approved
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