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

1,2

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

Table of n, a(n) for n=1..64.

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

Formula

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

Crossrefs

Cf. A039669.

Sequence in context: A136655 A060819 A318661 * A233526 A344674 A097062

Adjacent sequences: A089651 A089652 A089653 * A089655 A089656 A089657

Keyword

easy,nonn,tabf

Author

Philippe Deléham, Jan 04 2004

Status

approved