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A181741 Primes of the form 2^t-2^k-1, k>=1. 6
3, 5, 7, 11, 13, 23, 29, 31, 47, 59, 61, 127, 191, 223, 239, 251, 383, 479, 503, 509, 991, 1019, 1021, 2039, 3583, 3967, 4079, 4091, 4093, 6143, 8191, 15359, 16127, 16319, 16381, 63487, 65407, 65519, 129023, 131063, 131071, 245759, 253951, 261631, 261887, 262079, 262111, 262127, 262139 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

All Mersenne primes A000668(i) are in the sequence, parametrized by t=A000043(i)+1 and k=A000043(i).

If p is in the sequence, then the exponents t and k are unique.

For given k, the smallest value of t defines sequence A181692.

Every term p=2^t-2^k-1 in this sequence here generates an entry 2^(t-1)*p in A181595 (cf. A181701).

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000, probable primes for n > 150

Paul Pollack and Vladimir Shevelev, On perfect and near-perfect numbers, J. Number Theory 132 (2012), pp. 3037-3046. - N. J. A. Sloane, Sep 04 2012

V. Shevelev,Perfect and near-perfect numbers, arXiv:1011.6160 [math.NT], 2010-2012.

FORMULA

Conjecture: equals the intersection of A000040 and A081118 or the intersection of A000040 and A089633. [R. J. Mathar, Nov 18 2010]

MAPLE

isA000079 := proc(n) if n = 1 then true; elif type(n, 'odd') then false; else if nops( numtheory[factorset](n) ) = 1 then  true;  else

false; end if; end if; end proc:

isA181741 := proc(p) if isprime(p) then k := A007814(p+1) ; (p+1)/2^k+1 ; return ( isA000079(%) and k >=1 ) ; else

false;  end if; end proc:

for i from 1 to 1000 do p := ithprime(i) ; if isA181741(p) then printf("%d, ", p) ; end if; end do: # R. J. Mathar, Nov 18 2010

MATHEMATICA

Select[Table[2^t-2^k-1, {t, 1, 20}, {k, 1, t-1}] // Flatten // Union, PrimeQ] (* Jean-François Alcover, Nov 16 2017 *)

PROG

(Haskell)

a181741 n = a181741_list !! (n-1)

a181741_list = filter ((== 1) . a010051) a081118_list

-- Reinhard Zumkeller, Feb 23 2012

(PARI) lista(nn) = {for (n=3, nn, forstep(k=n-1, 1, -1, if (isprime(p=2^n-2^k-1), print1(p, ", ")); ); ); } \\ Michel Marcus, Dec 17 2018

CROSSREFS

Cf. A181595, A181692, A181701, A000043.

Cf. A010051, primes in A081118, see also A208083.

Sequence in context: A040140 A066651 A182583 * A154319 A080114 A088878

Adjacent sequences:  A181738 A181739 A181740 * A181742 A181743 A181744

KEYWORD

nonn

AUTHOR

Vladimir Shevelev, Nov 08 2010

EXTENSIONS

Corrected (251 and 1019 inserted) and extended by R. J. Mathar, Nov 18 2010

STATUS

approved

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Last modified September 21 07:08 EDT 2019. Contains 327253 sequences. (Running on oeis4.)