A089654 Table T(n,k), read by rows, related to a conjecture of P. Erdos (see A039669).

1, 3, 1, 5, 3, 7, 5, 1, 9, 7, 3, 11, 9, 5, 13, 11, 7, 15, 13, 9, 1, 17, 15, 11, 3, 19, 17, 13, 5, 21, 19, 15, 7, 23, 21, 17, 9, 25, 23, 19, 11, 27, 25, 21, 13, 29, 27, 23, 15, 31, 29, 25, 17, 1, 33, 31, 27, 19, 3, 35, 33, 29, 21, 5

Offset: 1

Author

Philippe Deléham, Jan 04 2004

Keywords

• easy
• nonn
• tabf

Comments

row n=1 : 1

row n=2 : 3, 1

row n=3 : 5, 3

row n=4 : 7, 5, 1

row n=5 : 9, 7, 3

row n=6 : 11, 9, 5

row n=7 : 13, 11, 7

row n=8 : 15, 13, 9, 1

row n=9 : 17, 15, 11, 3

P. Erdos conjectures that T(n,k) are all primes for n = 3, 7, 10, 22, 37, 52 and these are the only values of n with property . The conjecture has been verified for n up to 2^77. example : n=10; 19, 17, 13, 5 are all primes.

Links

• P. Erdős, On integers of the form 2^k + p and some related questions, Summa Bras. Math., 2 (1950), 113-123.

Crossrefs

Cf. A039669.

Formula

T(n, k) = 2*n+1-2^k, if T(n, k)>0.