A242116 -id:A242116

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A242175

Numbers n such that n*2^n + 1 is a semiprime.

+10
3

2, 3, 4, 5, 8, 9, 11, 16, 21, 33, 35, 101, 105, 131, 158, 165, 191, 234, 251, 435, 453, 459, 561, 579, 604, 671, 744, 753, 933, 963, 1041, 1146, 1168, 1254

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OFFSET

1,1

COMMENTS

The semiprimes of this form are 9, 25, 65, 161, 2049, 4609, 22529, ... (A242116).

a(35) >= 1528. Below 2000, 1794 and 1961 are in the sequence. Unknown factorization for 1528, 1576, 1908. - Hugo Pfoertner, Jul 29 2019

LINKS

Table of n, a(n) for n=1..34.

FactorDB, Status of 1528*2^1528+1.

FORMULA

A002064(a(n)) = A242116(n). - Amiram Eldar, Nov 27 2019

MATHEMATICA

Select[Range[165], Plus@@Last/@FactorInteger[# * 2^# + 1]==2&]

PROG

(Magma) IsSemiprime:=func<i | &+[d[2]: d in Factorization(i)] eq 2>; [n: n in [2..230] | IsSemiprime(s) where s is n*2^n+1]; // Bruno Berselli, May 08 2014

CROSSREFS

Cf. A001358, A002064, A005849, A242116, A242273.

KEYWORD

nonn,more,hard

AUTHOR

Vincenzo Librandi, May 07 2014

EXTENSIONS

a(17) from Bruno Berselli, May 08 2014

a(18)-a(30) from Luke March, Aug 13 2015

a(31)-a(34) from Hugo Pfoertner, Jul 29 2019

Wrong term 941 removed by Amiram Eldar, Nov 27 2019

STATUS

approved

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