A084213 -id:A084213 - cp's OEIS frontend

A001770 Numbers k such that 5*2^k - 1 is prime.

2, 4, 8, 10, 12, 14, 18, 32, 48, 54, 72, 148, 184, 248, 270, 274, 420, 1340, 1438, 1522, 1638, 1754, 1884, 2014, 2170, 2548, 2622, 2652, 2704, 13510, 21738, 25624, 41934, 51478, 52540, 53230, 172300, 245728, 350028, 1194164

Offset: 1

N. J. A. Sloane

A084213(a(n)+1) is in A136539, for all n. - Farideh Firoozbakht and M. F. Hasler, Nov 03 2012

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Y. Gallot, Proth.exe: Windows Program for Finding Large Primes
Wilfrid Keller, List of primes k.2^n - 1 for k < 300
H. C. Williams and C. R. Zarnke, A report on prime numbers of the forms M = (6a+1)*2^(2m-1)-1 and (6a-1)*2^(2m)-1, Math. Comp., 22 (1968), 420-422.
Index entries for sequences of n such that k*2^n-1 (or k*2^n+1) is prime

Cf. A002254 (5*2^n+1 is prime), A050522 (primes of the form 5*2^n - 1).

A001770:=n->`if`(isprime(5*2^n-1),n,NULL): seq(A001770(n), n=1..1000); # Wesley Ivan Hurt, Oct 15 2014

Select[Range[1000], PrimeQ[5*2^# - 1] &] (* Vaclav Kotesovec, Apr 28 2014 *)

is(n)=isprime(5*2^n-1) \\ Charles R Greathouse IV, Feb 07 2017

More terms from Hugo Pfoertner, Jun 23 2004

a(40) from the Wilfrid Keller link by Robert Price, Dec 22 2018

A136539 Numbers n such that n=6*phi(n)-sigma(n).

Original entry on oeis.org

76, 1264, 327424, 5241856, 83881984, 1342160896, 343597121536

Offset: 1

Farideh Firoozbakht, Jan 05 2008, Feb 01 2008

If 5*2^n-1 is prime (that is, n is in A001770) then m = 2^n*(5*2^n-1) is in the sequence. Proof: 6*phi(m)-sigma(m) = 6*2^(n-1)*(5*2^n-2) -(2^(n+1)-1)*5*2^n = 30*2^(2n-1)-6*2^n-5*2^(2n+1)+5*2^n = 5*2^(2n)-2^n = 2^n(5*2^n-1) = m.
The first seven terms of the sequence are of such form, with n=2, 4, 8, 10, 12, 14, 18. Are all terms of the sequence of this form?
a(8) > 10^12. - Giovanni Resta, Nov 03 2012

			6*phi(76)-sigma(76)=6*36-140=76 so 76 is in the sequence.

Cf. A001770, A136540.

Do[If[n==6*EulerPhi[n]-DivisorSigma[1,n],Print[n]],{n,85000000}]

a(n) = 2^k*(5*2^k-1) = A084213(k+1) with k = A001770(n), for n = 1,...,7. - M. F. Hasler, Nov 03 2012

a(7) from Giovanni Resta, Nov 03 2012

cp's OEIS Frontend

A001770 Numbers k such that 5*2^k - 1 is prime.

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