A005097 -id:A005097 - cp's OEIS frontend

A097363 Positive integers n such that 2n-13 is prime.

8, 9, 10, 12, 13, 15, 16, 18, 21, 22, 25, 27, 28, 30, 33, 36, 37, 40, 42, 43, 46, 48, 51, 55, 57, 58, 60, 61, 63, 70, 72, 75, 76, 81, 82, 85, 88, 90, 93, 96, 97, 102, 103, 105, 106, 112, 118, 120, 121, 123, 126, 127, 132, 135, 138, 141, 142, 145, 147, 148, 153, 160, 162

Offset: 1

Douglas Winston (douglas.winston(AT)srupc.com), Sep 18 2004

Shawn A. Broyles, Table of n, a(n) for n = 1..1000

Cf. A000040, A098602.
Numbers n such that 2n+k is prime: A005097 (k=1), A067076 (k=3), A089038 (k=5), A105760 (k=7), A155722 (k=9), A101448 (k=11), A153081 (k=13), A089559 (k=15), A173059 (k=17), A153143 (k=19).
Numbers n such that 2n-k is prime: A006254 (k=1), A098090 (k=3), A089253 (k=5), A089192 (k=7), A097069 (k=9), A097338 (k=11), this sequence (k=13), A097480 (k=15), A098605 (k=17), A097932 (k=19).

(Prime[Range[2,100]]+13)/2 (* Vladimir Joseph Stephan Orlovsky, Feb 08 2010 *)
Select[Range[8,200],PrimeQ[2#-13]&] (* Harvey P. Dale, Apr 26 2013 *)

Half of p+13 where p is a prime greater than 2.

A269254 To find a(n), define a sequence by s(k) = n*s(k-1) - s(k-2), with s(0) = 1, s(1) = n + 1; then a(n) is the smallest index k such that s(k) is prime, or -1 if no such k exists.

Original entry on oeis.org

1, 1, 2, 1, 2, 1, -1, 2, 2, 1, 2, 1, 2, -1, 2, 1, 3, 1, 2, 2, 2, 1, -1, 2, 6, 2, 3, 1, 3, 1, 2, 9, 9, -1, 2, 1, 6, 2, 2, 1, 2, 1, 5, 2, 2, 1, -1, 2, 5, 2, 9, 1, 2, 2, 2, 2, 6, 1, 2, 1, 14, -1, 5, 2, 2, 1, 5, 2, 3, 1, 6, 1, 8, 3, 6, 2, 3, 1, -1, 3, 18, 1, 2, 3, 2, 2, 3, 1, 2, 9, 3, 5, 2, 2, 96, 1, 3, -1, 5, 1, 2, 1, 2, 15, 14, 1, 44, 1, 3, -1

Offset: 1

Arkadiusz Wesolowski, Jul 09 2016

sign

The s(k) sequences can be viewed in A294099, where they appear as rows. - Peter Munn, Aug 31 2020
For n >= 3, a(n) is that positive integer k yielding the smallest prime of the form (x^y - 1/x^y)/(x - 1/x), where x = (sqrt(n+2) +- sqrt(n-2))/2 and y = 2*k + 1, or -1 if no such k exists.
Every positive term belongs to A005097.
When n=7, the sequence {s(k)} is A033890, which is Fibonacci(4i+2), and since x|y <=> F_x|F_y, and 2i+1|4i+2, A033890 is never prime, and so a(7)=-1. For the other -1 terms below 100, see the theorem below and the Klee link - N. J. A. Sloane, Oct 20 2017 and Oct 22 2017
Theorem (Brad Klee): For all n > 2, a(n^2 - 2) = -1. See Klee link for a proof. - L. Edson Jeffery, Oct 22 2017
Theorem (Based on work of Hans Havermann, L. Edson Jeffery, Brad Klee, Don Reble, Bob Selcoe, and N. J. A. Sloane) a(110) = -1. [For proof see link. - N. J. A. Sloane, Oct 23 2017]
From Bob Selcoe, Oct 24 2017, edited by N. J. A. Sloane, Oct 27 2017: (Start)
Suppose n = m^2 - 2, where m >= 3, and let j = m-2, with j >= 1.
For this value of n, the sequence s(k) satisfies s(k) = (c(k) + d(k))*(c(k) - d(k)), where c(0) = 1, d(0) = 0; and for k >= 1: c(k) = (j+2)*c(k-1) - d(k-1), and d(k) = c(k-1). So (as Brad Klee already proved) a(n) = -1 .
We have s(0) = 1 and s(1) = n+1 = j^2 + 4j + 3. In general, the coefficients of s(k) when expanded in powers of j are given by the (4k+2)-th row of A011973 (the triangle of coefficients of Fibonacci polynomials) in reverse order. For example, s(2) = j^4 + 8j^3 + 21j^2 + 20j + 5, s(3) = j^6 + 12j^5 + 55j^4 + 120j^3 + 126j^2 + 56j + 7, etc.
Perhaps the above comments could be generalized to apply to a(110) or to other n for which a(n) = -1?
(End)
For detailed theory, see [Hone]. - L. Edson Jeffery, Feb 09 2018

			Let b(k) be the recursive sequence defined by the initial conditions b(0) = 1, b(1) = 16, and the recursive equation b(k) = 15*b(k-1) - b(k-2). a(15) = 2 because b(2) = 239 is the smallest prime in b(k).
Let c(k) be the recursive sequence defined by the initial conditions c(0) = 1, c(1) = 18, and the recursive equation c(k) = 17*c(k-1) - c(k-2). a(17) = 3 because c(3) = 5167 is the smallest prime in c(k).

Hans Havermann, Table of n, a(n) for n = 1..946
Hans Havermann, Table of n, a(n) for n = 1..10000
C. K. Caldwell, Top Twenty page, Lehmer number
Andrew N. W. Hone, et al., On a family of sequences related to Chebyshev polynomials, arXiv:1802.01793 [math.NT], 2018.
Brad Klee, Proof for A269254, Sequence Fans Mailing List, October 2017.
N. J. A. Sloane et al., Proof that a(110) = -1
Wikipedia, Lehmer number.

Cf. A005097, A011973, A269251, A269252, A269253.
Cf. A294099 (array used to compute this sequence).
Cf. A285992, A299107, A299109, A088165, A117522, A299100, A299101, A113501, A298675, A298677, A298878, A299045, A299071.

lst:=[]; for n in [1..85] do if n gt 2 and IsSquare(n+2) then Append(~lst, -1); else a:=n+1; c:=1; t:=1; if IsPrime(a) then Append(~lst, t); else repeat b:=n*a-c; c:=a; a:=b; t+:=1; until IsPrime(a); Append(~lst, t); end if; end if; end for; lst;

kmax = 100;
a[1] = a[2] = 1;
a[n_ /; IntegerQ[Sqrt[n+2]]] = -1;
a[n_] := Module[{s}, s[0] = 1; s[1] = n+1; s[k_] := s[k] = n s[k-1] - s[k-2]; For[k=1, k <= kmax, k++, If[PrimeQ[s[k]], Return[k]]]; Print["For n = ", n, ", k = ", k, " exceeds the limit kmax = ", kmax]; -1];
Array[a, 110] (* Jean-François Alcover, Aug 05 2018 *)

allocatemem(2^30);
default(primelimit,(2^31)+(2^30));
s(n,k) = if(0==k,1,if(1==k,(1+n),((n*s(n,k-1)) - s(n,k-2))));
A269254(n) = { my(k=1); if((n>2)&&issquare(2+n),-1,while(!isprime(s(n,k)),k++);(k)); }; \\ Antti Karttunen, Oct 20 2017

If n is prime then a(n-1) = 1.

a(86)-a(94) from Antti Karttunen, Oct 20 2017

a(95)-a(109) appended by L. Edson Jeffery, Oct 22 2017

A104275 Numbers k such that 2k-1 is not prime.

Original entry on oeis.org

1, 5, 8, 11, 13, 14, 17, 18, 20, 23, 25, 26, 28, 29, 32, 33, 35, 38, 39, 41, 43, 44, 46, 47, 48, 50, 53, 56, 58, 59, 60, 61, 62, 63, 65, 67, 68, 71, 72, 73, 74, 77, 78, 80, 81, 83, 85, 86, 88, 89, 92, 93, 94, 95, 98, 101, 102, 103, 104, 105, 107, 108, 109, 110, 111, 113

Offset: 1

Alexandre Wajnberg, Apr 17 2005

Same as A053726 except for the first term of this sequence.
Numbers k such that A064216(k) is not prime. - Antti Karttunen, Apr 17 2015
Union of 1 and terms of the form (u+1)*(v+1) + u*v with 1 <= u <= v. - Ralf Steiner, Nov 17 2021

			a(1) = 1 because 2*1-1=1, not prime.
a(2) = 5 because 2*5-1=9, not prime (2, 3 and 4 give 3, 5 and 7 which are primes).
From _Vincenzo Librandi_, Jan 15 2013: (Start)
As a triangular array (apart from term 1):
   5;
   8,  13;
  11,  18,  25;
  14,  23,  32,  41;
  17,  28,  39,  50,  61;
  20,  33,  46,  59,  72,  85;
  23,  38,  53,  68,  83,  98, 113;
  26,  43,  60,  77,  94, 111, 128, 145;
  29,  48,  67,  86, 105, 124, 143, 162, 181;
  32,  53,  74,  95, 116, 137, 158, 179, 200, 221; etc.
which is obtained by (2*h*k + k + h + 1) with h >= k >= 1. (End)
The above array, which contains the same terms as A053726 but in different order and with some duplicates, has its own entry A144650. - _Antti Karttunen_, Apr 17 2015

Vincenzo Librandi (first 1000 terms) & Antti Karttunen, Table of n, a(n) for n = 1..10001

Cf. A006254 (complement), A246371 (a subsequence).

Cf. A005097, A008508, A014076, A047845, A053726, A064216, A144650.

[n: n in [1..220]| not IsPrime(2*n-1)]; // Vincenzo Librandi, Jan 28 2011

remove(t -> isprime(2*t-1), [$1..1000]); # Robert Israel, Apr 17 2015

Select[Range[115], !PrimeQ[2#-1] &] (* Robert G. Wilson v, Apr 18 2005 *)

select( {is_A104275(n)=!isprime(n*2-1)}, [1..115]) \\ M. F. Hasler, Aug 02 2022

from sympy import isprime
def ok(n): return not isprime(2*n-1)
print(list(filter(ok, range(1, 114)))) # Michael S. Branicky, May 08 2021

from sympy import primepi
def A104275(n):
    if n <= 2: return ((n-1)<<2)+1
    m, k = n-1, (r:=primepi(n-1)) + n - 1 + (n-1>>1)
    while m != k:
        m, k = k, (r:=primepi(k)) + n - 1 + (k>>1)
    return r+n-1 # Chai Wah Wu, Aug 02 2024

[n for n in (1..250) if not is_prime(2*n-1)] # G. C. Greubel, Oct 17 2023

(define (A104275 n) (if (= 1 n) 1 (A053726 (- n 1)))) ;; More code in A053726. - Antti Karttunen, Apr 17 2015

a(n) = A047845(n-1) + 1.
For n > 1, a(n) = A053726(n-1) = n + A008508(n-1). - Antti Karttunen, Apr 17 2015
a(n) = (A014076(n)+1)/2. - Robert Israel, Apr 17 2015

More terms from Robert G. Wilson v, Apr 18 2005

A102781 Number of positive even numbers less than the n-th prime.

Original entry on oeis.org

0, 1, 2, 3, 5, 6, 8, 9, 11, 14, 15, 18, 20, 21, 23, 26, 29, 30, 33, 35, 36, 39, 41, 44, 48, 50, 51, 53, 54, 56, 63, 65, 68, 69, 74, 75, 78, 81, 83, 86, 89, 90, 95, 96, 98, 99, 105, 111, 113, 114, 116, 119, 120, 125, 128, 131, 134, 135, 138, 140, 141, 146, 153, 155, 156

Offset: 1

Cino Hilliard, Feb 25 2005

Same as A005097 ((odd primes - 1)/2) with a leading zero. - Lambert Klasen, Nov 06 2005

Ray Chandler, Table of n, a(n) for n = 1..10000

Cf. A005097. - R. J. Mathar, May 18 2009

Equals (A000040-1)/2, integer part (0) for the first term. - M. F. Hasler, Dec 13 2019

Table[Prime[n] - Floor[Prime[n]/2] - 1, {n, 65}] (* Robert G. Wilson v *)

c(n,r) = { local(p); forprime(p=r,n, print1(floor(primorial(p)/ primorial(p-r)/primorial(r)+.0)",") ) } primorial(n) = \ The product primes <= n using the pari primelimit. { local(p1,x); if(n==0||n==1, return(2)); p1=1; forprime(x=2,n,p1*=x); return(p1) }

apply( A102781(n)=(prime(n)-1)\2, [1..99]) \\ M. F. Hasler, Dec 13 2019

from sympy import prime
def A102781(n): return prime(n)-1>>1 # Chai Wah Wu, Oct 13 2024

Integer part of p#/((p-2)#*2#), where p=prime(n) and i# is the primorial function A034386(i). - Cino Hilliard, Feb 25 2005
n# = product of primes <= n. 0# = 1# = 2. [This is not a standard convention!] n#/(n-r)#/r# is analogous to the number of binomial coefficients A007318 = C(n, r) = n!/(n-r)!/r! where factorial ! is replaced by primorial #.
a(n) = prime_n - floor((prime_n)/2) - 1. - Giovanni Teofilatto, Nov 05 2005
a(n) = [A034386(prime(n))/(2*A034386(prime(n)-2))], n>2. - R. J. Mathar, May 18 2009
a(n) = [(prime(n)-1)/2] where the integer part [.] needs be taken only for n=1. - M. F. Hasler, Dec 13 2019

Simpler definition from Giovanni Teofilatto, Nov 05 2005

Edited by N. J. A. Sloane Jul 05 2009 at the suggestion of R. J. Mathar

A123998 Numbers k such that 2k+1 and 4k+1 are primes.

Original entry on oeis.org

1, 3, 9, 15, 18, 39, 48, 69, 78, 99, 105, 114, 135, 153, 165, 168, 183, 189, 219, 249, 273, 288, 300, 303, 309, 330, 345, 363, 405, 414, 438, 468, 483, 498, 504, 534, 585, 618, 639, 648, 699, 714, 729, 765, 804, 813, 828, 879, 933, 1005, 1014, 1044, 1065, 1068

Offset: 1

Artur Jasinski, Oct 31 2006

Note that if n == 1 (mod 3) then 2n+1 is not prime (except n=1); and if n == 2 (mod 3) then 4n+1 is not prime. Therefore n must be a multiple of 3, except for n=1. - Max Alekseyev, Nov 02 2006

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
J. O'Rourke, Why are this operator's primes the Sophie Germain primes?

Cf. A005097, A005098, A124408, A124409, A124410, A124411, A071576.

[n: n in [0..1100] |IsPrime(2*n+1) and IsPrime(4*n+1)]; // Vincenzo Librandi, Apr 17 2013

Select[Range[1100], And @@ PrimeQ /@ ({2, 4}*# + 1) &] (* Ray Chandler, Nov 20 2006 *)

is(k) = isprime(2*k+1) && isprime(4*k+1); \\ Jinyuan Wang, Aug 04 2019

Extended by Ray Chandler, Nov 20 2006

A016017 Smallest k such that 1/k can be written as a sum of exactly 2 unit fractions in n ways.

Original entry on oeis.org

1, 2, 4, 8, 6, 32, 64, 12, 256, 512, 24, 2048, 36, 30, 16384, 32768, 96, 72, 262144, 192, 1048576, 2097152, 60, 8388608, 216, 768, 67108864, 288, 1536, 536870912, 1073741824, 120, 576, 8589934592, 6144, 34359738368, 68719476736, 180, 864

Offset: 1

Robert G. Wilson v

nonn

From Jianing Song, Aug 30 2021: (Start)
a(n) is the smallest number whose square has exactly 2n-1 divisors.
a(n) is the earliest occurrence of 2n-1 in A048691. (End)

			a(1)=1 and a(2)=2 because 1/2 = 1/3 + 1/6 = 1/4 + 1/4.
a(3)=4 because 1/4 = 1/5 + 1/20 = 1/6 + 1/12 = 1/8 + 1/8.
a(4)=8 because 1/8 = 1/9 + 1/72 = 1/10 + 1/40 = 1/12 + 1/24 = 1/16 + 1/16.
a(5)=6 because 1/6 = 1/7 + 1/42 = 1/8 + 1/24 = 1/9 + 1/18 = 1/10 + 1/15 = 1/12 + 1/12.

David W. Wilson, Table of n, a(n) for n = 1..1000 (terms 122, 365 and 608 corrected by _Amiram Eldar_, Nov 08 2024)

Identical to A071571 shifted right.

Cf. A000005, A000290, A005408, A005179, A003680, A037992, A055079, A048691.

f[j_, n_] := (Times @@ (j(Last /@ FactorInteger[n]) + 1) + j - 1)/j; t = Table[0, {50}]; Do[a = f[2, n]; If[a < 51 && t[[a]] == 0, t[[a]] = n; Print[{a, n}]], {n, 2^30}] (* Robert G. Wilson v, Aug 03 2005 *)

a(n) = {k = 1; while (numdiv(k^2) != (2*n-1), k++); return (k); }; \\ Amiram Eldar, Jan 07 2019 after Michel Marcus at A071571

a(n+1) <= 2^n.
From Labos Elemer, May 22 2001: (Start)
a(n) = sqrt(A061283(n)).
a(n) = sqrt(Min{k| A000005(k)=2n-1}).
a((p+1)/2) = 2^((p-1)/2) = 2^A005097(i) if p is the i-th odd prime. [Corrected by Jianing Song, Aug 30 2021] (End)
a(n) is the least k such that (tau(k^2) + 1)/2 = n. - Vladeta Jovovic, Aug 01 2001

Entry revised by N. J. A. Sloane, Aug 14 2005

Offset corrected by David W. Wilson, Dec 27 2018

A071576 a(n) = least k such that 2ik + 1 is prime for all 1 <= i <= n.

Original entry on oeis.org

1, 1, 1, 165, 5415, 12705, 256410, 256410, 6480303060, 217245863835, 946622690475, 35511547806735, 439116128090640, 5714676453270219435

Offset: 1

Benoit Cloitre, May 31 2002

Cf. A088250, A124516, A124522, A124522, A063983.

Cf. A005097, A123998, A124408-A124411.

k = 1; Do[ While[p = Table[2*i*k + 1, {i, 1, n}]; Union[ PrimeQ[p]] != {True}, k++ ]; Print[k], {n, 1, 15}] (* Robert G. Wilson v *)

for(n=1,6,s=1; while(sum(i=1,n,isprime(2*s*i+1))

Extended by Robert G. Wilson v, Jun 06 2002
a(9) from Ryan Propper, Jun 20 2005
a(10)-a(13) from Don Reble, Nov 05 2006
a(14) from Giovanni Resta, Apr 01 2017

A084712 Smallest prime of the form (2n)^k + 1, or 0 if no such number exists.

Original entry on oeis.org

3, 5, 7, 0, 11, 13, 197, 17, 19, 401, 23, 577, 677, 29, 31, 0, 1336337, 37

Offset: 1

Amarnath Murthy, Jun 10 2003

It has not been proved that a(19), a(25), a(31), a(34), a(43) and a(46) are 0; if these values do exist, they have > 4000 digits. The other zeros are definite. - David Wasserman, Jan 03 2005
a((p-1)/2) = p for primes p > 2, or a(n) = 2n+1 for n = (p-1)/2. All other positive a(n) belong to A002496 = primes of form m^2 + 1. Corresponding positive exponents k are powers of 2. They are listed in A079706. - Alexander Adamchuk, Sep 17 2006
Because k must be a power of 2, numbers of the form (2n)^k+1 are called generalized Fermat numbers with base 2n. These numbers, like the regular Fermat numbers, are seldom prime. I checked n=19, 25, 31, 34, 43, 46 with k up to 2^16 without finding any primes. - T. D. Noe, May 13 2008
Comments from N. J. A. Sloane, Jan 27 2024: (Start)
As pointed out by Max Alekseyev, the previous version violated the OEIS rules, since a(19) has not been confirmed. I therefore removed the terms starting at a(19).
The previous DATA line read:
3, 5, 7, 0, 11, 13, 197, 17, 19, 401, 23, 577, 677, 29, 31, 0, 1336337, 37, 0, 41, 43, 197352587024076973231046657, 47, 5308417, 0, 53, 2917, 3137, 59, 61, 0, 0, 67, 0, 71, 73, 5477, 1238846438084943599707227160577, 79, 40960001, 83, 7057, 0, 89
The old b-file has been changed to an a-file.
(End)

			a(7) = 197 = 14^2 + 1 as 14 + 1 = 15 is not a prime.

Vincenzo Librandi, Table of n, a(n) for n = 1..500 (currently known terms, may contain 0s in place of unknown terms)

Cf. A084713, A005097.

Table[k=1; While[p=1+(2n)^k; k<1024 && !PrimeQ[p], k=2k]; If[k==1024, 0, p], {n,44}] (* T. D. Noe, May 13 2008 *)

More terms from David Wasserman, Jan 03 2005

Edited by N. J. A. Sloane, Jan 27 2024 at the suggestion of Max Alekseyev

A098006 (p-1)/2 - phi(p-1) as p runs through the odd primes.

Original entry on oeis.org

0, 0, 1, 1, 2, 0, 3, 1, 2, 7, 6, 4, 9, 1, 2, 1, 14, 13, 11, 12, 15, 1, 4, 16, 10, 19, 1, 18, 8, 27, 17, 4, 25, 2, 35, 30, 27, 1, 2, 1, 42, 23, 32, 14, 39, 57, 39, 1, 42, 4, 23, 56, 25, 0, 1, 2, 63, 50, 44, 49, 2, 57, 35, 60, 2, 85, 72, 1, 62, 16, 1, 63, 66, 81, 1, 2, 78, 40, 76, 29, 114, 47

Offset: 2

N. J. A. Sloane, Sep 08 2004

In the Luca-Walsh paper it is shown that there are infinitely many numbers not in this sequence. See A098047.

a(n)=0 for Fermat primes (A019434). a(n)=1 for safe primes (A005385). a(n)=2 for A090866. The least prime p for which (p-1)/2-phi(p-1)=n or 0 if there is no such prime is given by A134765(n). Sequence A134854(k) gives the least prime for which a(n)=2^(k-1). For k not a power of 2, it can be shown that if k is in this sequence, then it appears for a prime p <= 1+k^2. - T. D. Noe, Nov 13 2007

J. Browkin and A. Schinzel, On integers not of the form n-phi(n), Colloq. Math., 68 (1995), 55-58.
F. Luca and P. G. Walsh, On the number of nonquadratic residues which are not primitive roots, Colloq. Math., 100 (2004), 91-93.

T. D. Noe, Table of n, a(n) for n = 2..10000
T. D. Noe, Finding primes p for which (p-1)/2 - phi(p-1) = k

Cf. A000010, A051953, A098047, A176095 (p runs through the odd numbers).

a098006 n = a005097 (n-1) - a000010 (a006093 n)
-- Reinhard Zumkeller, Mar 26 2013

[(NthPrime(n)-1)/2 - EulerPhi(NthPrime(n)-1): n in [2..100]]; // Vincenzo Librandi, Jan 10 2017

A098006 := proc(n)
    local p;
    p := ithprime(n+1) ;
    (p-1)/2-numtheory[phi](p-1) ;
end proc:
seq(A098006(n),n=1..30) ; # R. J. Mathar, Jan 09 2017

Table[(Prime[n] - 1)/2 - EulerPhi[Prime[n] - 1], {n, 2, 85}] (* Robert G. Wilson v, Sep 09 2004 *)
Table[(n-1)/2-EulerPhi[n-1],{n,Prime[Range[2,100]]}] (* Harvey P. Dale, Oct 23 2016 *)

forprime(p=3,1e3,print1(p\2-eulerphi(p-1)", ")) \\ Charles R Greathouse IV, Feb 04 2013

a(n) = A005097(n-1) - A000010(A006093(n)); a(A159611(n)) = 0. - Reinhard Zumkeller, Mar 26 2013

A124417 a(n) = least k such that 2^i*k+1 is prime for 1<=i<=n.

Original entry on oeis.org

1, 1, 9, 765, 765, 8325, 8325, 7757430, 428547690, 102764221560, 694561346985, 108428872433310, 379041973928475, 34628781572140470, 34628781572140470

Offset: 1

Artur Jasinski, Nov 02 2006

Cf. A005097, A123998, A124041, A124412, A124413, A124414, A124415, A124416.

k = 1; Do[If[n < 3, inc = 1,If[n == 3, inc = 3, inc = 15];];If[Mod[k, inc] > 0, k = k + inc - Mod[k, inc]];While[Nand @@ PrimeQ[Table[2^j, {j, n}]*k + 1], k += inc]; Print[k], {n, 1, 15}] (* Ray Chandler, Nov 21 2006 *)

Edited by Ray Chandler, Nov 21 2006
a(10) from Farideh Firoozbakht, Nov 25 2006
a(11)-a(15) from Giovanni Resta, Apr 24 2019

cp's OEIS Frontend

A097363 Positive integers n such that 2n-13 is prime.

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A269254 To find a(n), define a sequence by s(k) = n*s(k-1) - s(k-2), with s(0) = 1, s(1) = n + 1; then a(n) is the smallest index k such that s(k) is prime, or -1 if no such k exists.

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A104275 Numbers k such that 2k-1 is not prime.

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A102781 Number of positive even numbers less than the n-th prime.

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A123998 Numbers k such that 2k+1 and 4k+1 are primes.

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A016017 Smallest k such that 1/k can be written as a sum of exactly 2 unit fractions in n ways.

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