A292911 Numbers n such that A291897(n) is divisible by (2*n-1)^3.

1, 3, 7, 9, 15, 19, 21, 27, 31, 37, 45, 49, 51, 55, 57, 69, 75, 79, 87, 91, 97, 99, 115, 117, 121, 129, 135, 139, 141, 147, 157, 159, 169, 175, 177, 187, 195, 199, 201, 205, 211, 217, 225, 229, 231, 255, 261, 271, 279, 285, 289, 297, 301, 307, 309, 321, 327

Offset: 1

Author

Vladimir Shevelev, Sep 26 2017

Keywords

• nonn

Comments

Conjecture: Every prime of the form 4*k+1 (A002144) is contained in the sequence {2*a(n)-1}.

The author's former conjecture that, for n>=2 the numbers {2*a(n)-1} are consecutive primes of the form 4*k+1, was disproved at n = 553 by Peter J. C. Moses. (553*2 - 1 = 1105 is the smallest term which is a product of three distinct (4*k+1)-primes). - Vladimir Shevelev, Sep 27 2017

553 is also (after 1) the smallest number which is missing from A119681 but is present here. - R. J. Mathar, Sep 29 2017

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..500
• Michael De Vlieger, Comparison of A292911 and A002144

Crossrefs

Cf. A002144, A291897.

Programs

Mathematica

Select[Array[{2^IntegerExponent[2 #, 2] EulerE[2 # - 1, #], #} &, 330], Divisible[#1, (2 #2 - 1)^3] & @@ # &][[All, -1]] (* Michael De Vlieger, Sep 27 2017, after Peter Luschny at A291897 *)

Formula

If the conjecture is true, then for n>=2, a(n) <= (A002144(n-1) + 1)/2 (the equality holds up to 90).

Extensions

More terms from Peter J. C. Moses, Sep 26 2017