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, 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

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 * A334052 A160570 A128830

Adjacent sequences: A286654 A286655 A286656 * A286658 A286659 A286660

Keyword

nonn,tabl

Author

Rémy Sigrist, May 14 2017

Status

approved