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A286657 Triangle read by rows. T(n,k) = least m > 0 such that prime(n) + m * prime(k) and m * prime(n) + prime(k) are both prime numbers, 1 <= k < n. 1
1, 1, 2, 3, 2, 2, 1, 4, 6, 6, 3, 2, 2, 4, 6, 1, 2, 4, 2, 4, 2, 5, 4, 2, 4, 8, 4, 14, 3, 10, 4, 2, 4, 6, 12, 6, 1, 10, 6, 6, 4, 14, 6, 8, 6, 5, 4, 2, 4, 2, 4, 24, 18, 14, 8, 3, 10, 2, 6, 6, 10, 6, 4, 2, 6, 10, 1, 4, 6, 20, 6, 14, 4, 2, 6, 4, 2, 6, 9, 8, 6, 4, 6 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

The triangle T(n,k) begins:

n\k  1  2  3  4  5  6  7  8  9

1:

2:   1

3:   1  2

4:   3  2  2

5:   1  4  6  6

6:   3  2  2  4  6

7:   1  2  4  2  4  2

8:   5  4  2  4  8  4 14

9:   3 10  4  2  4  6 12  6

10:  1 10  6  6  4 14  6  8  6

Assuming Dickson's conjecture, T(n,k) always exists.

T(n,1) is odd.

T(n,k) is even for any k > 1.

A229980(n) = T(n+1, n) for any n > 0.

LINKS

Rémy Sigrist, Rows n=1..100 of triangle, flattened

OEIS Wiki, Dickson's conjecture

EXAMPLE

prime(7) + m*prime(11) is prime for m = 2,  12,        24, 26, 30, ...

m*prime(7) + prime(11) is prime for m =   8,   14, 18, 24,     30, ...

Hence, T(11,7) = 24.

PROG

(PARI) t(n, k) = my (pn=prime(n), pk=prime(k), i=1); while (!isprime(pn+i*pk) || !isprime(i*pn+pk), i++); return (i)

CROSSREFS

Cf. A229980.

Sequence in context: A152197 A049342 A112966 * A160570 A128830 A090387

Adjacent sequences:  A286654 A286655 A286656 * A286658 A286659 A286660

KEYWORD

nonn,tabl

AUTHOR

Rémy Sigrist, May 14 2017

STATUS

approved

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Last modified March 19 13:08 EDT 2019. Contains 321330 sequences. (Running on oeis4.)