A126661 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.

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

Offset

1,1

Comments

Two-dimensional analog of 1-dimensional semiprime-derived A126608.

Links

Table of n, a(n) for n=1..99.

Formula

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

Example

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.

Maple

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

Crossrefs

Cf. A000040, A126608-A126609, A126660.

Sequence in context: A192451 A129856 A136800 * A162226 A001650 A130175

Adjacent sequences: A126658 A126659 A126660 * A126662 A126663 A126664

Keyword

easy,tabl,nonn

Author

Jonathan Vos Post, Feb 10 2007

Extensions

Edited by R. J. Mathar, Feb 13 2007

Status

approved