A369901 Proth numbers h*2^k+1, with odd h < 2^k, ordered first by k then by h.

3, 5, 13, 9, 25, 41, 57, 17, 49, 81, 113, 145, 177, 209, 241, 33, 97, 161, 225, 289, 353, 417, 481, 545, 609, 673, 737, 801, 865, 929, 993, 65, 193, 321, 449, 577, 705, 833, 961, 1089, 1217, 1345, 1473, 1601, 1729, 1857, 1985, 2113, 2241, 2369, 2497, 2625, 2753, 2881

Offset

1,1

Links

Daniel Sturm, Table of n, a(n) for n = 1..1023

David A. Corneth, PARI program.

E. Proth, Théorèmes sur les nombres premiers, Comptes rendus hebdomadaires des séances de l'Académie des sciences, 1878, p. 926.

Wikipedia, Proth Primes.

Formula

a(2^b+c) = (2c+1)*2^(b+1) for 0 <= c < 2^b.

Example

Displayed as an irregular triangle:
  3;
  5, 13;
  9, 25, 41, 57;
  17, 49, 81, 113, 145, 177, 209, 241;
  ...

Prog

(Python)
def A369901(n):
    b = n.bit_length() - 1
    c = n - 2**b
    return (2*c+1)*2**(b+1)+1
(PARI) \\ See PARI link

Crossrefs

Cf. A080075 (Proth numbers).

Cf. A000051 (1st column), A020515 (right diagonal).

Sequence in context: A348744 A263829 A028268 * A171424 A231897 A260416

Adjacent sequences: A369898 A369899 A369900 * A369902 A369903 A369904

Keyword

nonn,easy,tabf

Author

Daniel Sturm, Feb 05 2024

Extensions

More terms from David A. Corneth, Feb 05 2024

Status

approved