Vardan Semerjyan - cp's OEIS frontend

A270102 Numbers k such that 3^k - k*2^k is prime.

3, 4, 5, 7, 8, 10, 11, 23, 34, 62, 95, 128, 173, 251, 260, 464, 628, 1267, 1895, 2057, 2743, 5102, 7790, 49163

Offset: 1

Vardan Semerjyan, Mar 11 2016

a(25) > 10^5. - Michael S. Branicky, Oct 13 2024

			n = 4 is a term since 3^4 - 4*2^4 = 17 is prime.

Cf. A057468, A270104.

MATLAB
```
if isprime(3^n - n*2^n)
disp(n)
end
```

A270102:=n->`if`(isprime(3^n-n*2^n),n,NULL): seq(A270102(n),n=1..2000); # Wesley Ivan Hurt, May 08 2016

Select[Range[1, 1000], PrimeQ[3^# - #*2^#] &] (* Vaclav Kotesovec, Mar 11 2016 *)

is(n)=ispseudoprime(3^n-n*2^n) \\ Charles R Greathouse IV, Jun 06 2017

from gmpy2 import is_prime
for n in range(5000):
   if(is_prime(3**n-n*2**n)):print(n,end=", ")
# Soumil Mandal, May 08 2016

a(24) from Giovanni Resta, May 05 2016

A270104 Numbers k such that 3^k + k*2^k is prime.

Original entry on oeis.org

1, 2, 7, 8, 13, 43, 55, 59, 145, 149, 545, 2468, 4049, 4055, 15653, 22765, 99932

Offset: 1

Vardan Semerjyan, Mar 11 2016

a(17) > 30000. - Giovanni Resta, May 05 2016

			n = 2 is a term since 3^2 + 2*2^2 = 17 is prime.

Cf. A270102, A123924.

MATLAB
```
if isprime(3^n + n*2^n)
disp(n)
end
```

Select[Range[1000], PrimeQ[3^# + # * 2^#]&] (* Giovanni Resta, May 05 2016 *)

is(n)=ispseudoprime(3^n+n*2^n) \\ Charles R Greathouse IV, Jun 13 2017

a(15)-a(16) from Giovanni Resta, May 05 2016

a(17) from Michael S. Branicky, Jul 06 2024

A265505 Numbers n such that n*2^107 - 1 is prime.

Original entry on oeis.org

1, 25, 36, 81, 246, 273, 358, 378, 595, 658, 684, 703, 706, 739, 759, 883, 909, 958, 963, 970, 991, 1014, 1054, 1138, 1189, 1200, 1209, 1356, 1359, 1476, 1488, 1534, 1554, 1590, 1594, 1684, 1695, 1719, 1785, 1791, 1858, 1929, 2008, 2094, 2103, 2115, 2146, 2224, 2229, 2266, 2278, 2283, 2313, 2325, 2380, 2388, 2401

Offset: 1

Vardan Semerjyan, Dec 09 2015

nonn

The exponent of 2 in the expression, 107, is a Mersenne exponent.

			n = 1 is a term since 2^107 - 1 is prime (the 11th Mersenne prime).

Cf. A000043, A001348, A005122, A265497, A265502, A265503, A265504.

MATLAB
```
if isprime(n*2^107-1)
disp(n)
end
```

Select[Range@ 2401, PrimeQ[# 2^107 - 1] &] (* Michael De Vlieger, Dec 16 2015 *)

is(n)=ispseudoprime(n*2^107- 1) \\ Anders Hellström, Dec 16 2015

A265504 Numbers n such that n*2^2281 - 1 is prime.

Original entry on oeis.org

1, 1144, 4027, 7485, 9039, 9940, 11286, 11781, 13095, 13236, 13869, 14124, 14764, 16630, 18075, 18795, 19284, 20797, 21436, 22696, 23904, 25297, 25419, 27391, 27564, 28146, 28392, 29865, 30624, 31087, 31137, 31369, 33286, 33724, 33741, 34609, 34837, 35034, 37047, 37075, 39564, 39910, 41181

Offset: 1

Vardan Semerjyan, Dec 09 2015

nonn

The exponent of 2 in the expression, 2281, is a Mersenne exponent.

All large values of n correspond to pseudoprimes whose primality needs to be verified.

			n = 1 is a term since 2^2281 - 1 is prime (the 17th Mersenne prime).

Cf. A000043, A001348, A005122.

MATLAB
```
if isprime(n*2^2281-1)
disp(n)
end
```

[n: n in [1..10^4] |IsPrime(n*2^2281-1)]; // Vincenzo Librandi, Jan 12 2016

Select[Range[10^4], PrimeQ[2^2281 # - 1] &] (* Vincenzo Librandi, Jan 12 2016 *)

is(n)=ispseudoprime(n*2^2281 - 1) \\ Anders Hellström, Dec 16 2015

More terms from Soumadeep Ghosh, Feb 14 2016

A265503 Numbers n such that n*2^2203 - 1 is prime.

Original entry on oeis.org

1, 13, 553, 861, 1983, 2065, 2403, 4371, 6226, 6553, 6580, 10128, 10998, 11193, 12411, 12598, 12909, 13056, 13194, 13399, 14589, 15829, 18429, 18436, 19315, 19900, 21574, 23599, 24006, 24024, 24415, 25704, 27225, 27651, 28689, 29461, 29805, 29868, 31143, 31186, 32674, 33706, 34306, 35016, 36118

Offset: 1

Vardan Semerjyan, Dec 09 2015

nonn

The exponent of 2 in the expression, 2203, is a Mersenne exponent.

			n = 1 is a term since 2^2203 - 1 is prime (the 16th Mersenne prime).

Cf. A000043, A001348, A005122.

MATLAB
```
if isprime(n*2^2203-1)
disp(n)
end
```

[n: n in [1..7*10^3] |IsPrime(n*2^2203-1)]; // Vincenzo Librandi, Dec 10 2015

Select[Range@ 36200, PrimeQ[# 2^2203 - 1] &] (* Michael De Vlieger, Dec 09 2015 *)

is(n)=ispseudoprime(n*2^2203-1) \\ Anders Hellström, Dec 09 2015

More terms from Michael De Vlieger, Dec 09 2015

A265502 Numbers n such that n*2^1279 - 1 is prime.

Original entry on oeis.org

1, 139, 433, 1563, 2095, 2254, 2871, 3751, 4003, 4338, 4843, 6015, 6331, 6933, 7324, 7345, 7485, 7719, 7836, 8070, 8413, 9018, 9840, 9898, 9915, 9931, 10611, 11215, 11356, 11418, 11560, 11740, 12010, 12673, 13039, 13056, 13225, 14136, 14271, 14380, 14974, 15084

Offset: 1

Vardan Semerjyan, Dec 09 2015

nonn

The exponent of 2 in the expression, 1279, is a Mersenne exponent.

			n = 1 is a term since 2^1279 - 1 is prime (the 15th Mersenne prime).

Andrew Howroyd, Table of n, a(n) for n = 1..1000

Cf. A000043, A001348, A005122.

MATLAB
```
if isprime(n*2^1279-1)
disp(n)
end
```

[n: n in [1..10^4] |IsPrime(n*2^1279-1)]; // Vincenzo Librandi, Dec 10 2015

Select[Range@ 11500, PrimeQ[# 2^1279 - 1] &] (* Michael De Vlieger, Dec 09 2015 *)

is(n)=ispseudoprime(n*2^1279 - 1) \\ Anders Hellström, Dec 09 2015

Terms a(31) and beyond from Andrew Howroyd, Dec 23 2019

A265499 Numbers n such that n*2^607 - 1 is prime.

Original entry on oeis.org

1, 226, 273, 544, 675, 961, 1380, 1968, 2155, 2193, 2596, 3481, 3774, 4074, 4513, 4674, 4866, 4899, 5004, 5418, 5421, 5536, 5815, 5949, 6159, 6249, 6390, 6523, 6526, 6543, 7230, 7281, 7645, 7699, 7968, 8473, 8518, 8724, 8763, 8871, 9519, 9780, 9805

Offset: 1

Vardan Semerjyan, Dec 09 2015

The exponent of 2 in the expression, 607, is a Mersenne exponent.

			n = 1 is a term since 2^607 - 1 is prime (the 14th Mersenne prime).

Cf. A000043, A001348, A005122.

MATLAB
```
if isprime(n*2^607-1)
disp(n)
end
```

[n: n in [1..2*10^4] |IsPrime(n*2^607-1)]; // Vincenzo Librandi, Dec 10 2015

Select[Range@ 12250, PrimeQ[# 2^607 - 1] &] (* Michael De Vlieger, Dec 09 2015 *)

is(n)=ispseudoprime(n*2^607 - 1) \\ Anders Hellström, Dec 09 2015

A265498 Numbers n such that n*2^521 - 1 is prime.

Original entry on oeis.org

1, 1362, 1756, 1905, 2337, 2707, 2902, 2997, 3487, 3492, 3787, 3879, 4045, 4266, 4374, 4680, 5106, 5691, 5766, 6321, 6352, 6585, 6819, 7056, 7099, 7162, 7470, 7627, 8055, 8061, 8121, 8499, 8511, 8785, 8865, 9432, 9636, 9876, 10116, 10389, 10629, 10752, 11262

Offset: 1

Vardan Semerjyan, Dec 09 2015

The exponent of 2 in the expression, 521, is a Mersenne exponent.

			n = 1 is a term since 2^521-1 is prime (13th Mersenne prime).

Cf. A000043, A001348, A005122.

MATLAB
```
if isprime(n*2^521-1)
disp(n)
end
```

[n: n in [1..2*10^4] |IsPrime(n*2^521-1)]; // Vincenzo Librandi, Dec 10 2015

Select[Range@ 12050, PrimeQ[# 2^521 - 1] &] (* Michael De Vlieger, Dec 09 2015 *)

is(n) = ispseudoprime(n*2^521 - 1); \\ Altug Alkan, Dec 10 2015

A265497 Numbers n such that n*2^127 - 1 is prime.

Original entry on oeis.org

1, 103, 190, 289, 460, 483, 511, 534, 651, 793, 820, 880, 901, 939, 945, 958, 1045, 1168, 1195, 1198, 1216, 1374, 1408, 1479, 1489, 1500, 1521, 1534, 1539, 1569, 1599, 1623, 1630, 1671, 1678, 1875, 1938, 1939, 1963, 1996, 2028, 2136, 2140, 2166, 2179, 2289

Offset: 1

Vardan Semerjyan, Dec 09 2015

The exponent of 2 in the expression, 127, is a Mersenne exponent.

			n = 1 is a term since 2^127 - 1 is prime (the 12th Mersenne prime).

Cf. A000043, A001348, A005122.

MATLAB
```
if isprime(n*2^127-1)
disp(n)
end
```

[n: n in [1..3*10^3] |IsPrime(n*2^127-1)]; // Vincenzo Librandi, Dec 10 2015

Select[Range@ 2560, PrimeQ[# 2^127 - 1] &] (* Michael De Vlieger, Dec 09 2015 *)

is(n)=ispseudoprime(n*2^127 - 1) \\ Anders Hellström, Dec 09 2015

A257749 Prime numbers that have a dodecagonal (12 sides) Voronoi cell in the Voronoi diagram of the Ulam prime spiral.

Original entry on oeis.org

61673, 635939, 706117, 720743, 1483439, 1742501, 1766701, 1847603, 2097959, 2163461, 2365289, 2429411, 3420101, 3490703, 3657361, 3920843, 3973829, 4758973, 4920887, 4989779, 5273753, 6167687, 6223247, 6573559, 6655409, 6694333, 6791881, 7095503, 7102349, 7338293, 7644541

Offset: 1

Vardan Semerjyan, May 07 2015

nonn

Vardan Semerjyan, Voronoi diagram of prime spiral

Cf. A257527, A257528, A000040.

sz  = 3001; % Size of the N x N square matrix
mat = spiral(sz); % MATLAB Function
k = 1;
for i =1:sz
    for j=1:sz
        if isprime(mat(i,j)) % Check if the number is prime
            % saving indices of primes
            y(k) = i; x(k) = j;
            k = k+1;
        end
    end
end
xy = [x',y'];
[v,c] = voronoin(xy); %  Returns Voronoi vertices V and
% the Voronoi cells C
k = 1;
for i = 1:length(c)
  szv = size(v(c{i},1));
  polyN(i) = szv(1);
  if polyN(i) == 12
        A(k) = mat(y(i),x(i));
        k = k+1;
      end
end
% Print terms
A = sort(A);
fprintf('A = ');
fprintf('%i, ',A);
% When running the code be aware that the last terms you get might not be correct.
% They correspond to the points on the outer edges of the spiral which might be
% altered when considering a larger spiral.
% Use larger spiral to get more terms

cp's OEIS Frontend

User: Vardan Semerjyan

A270102 Numbers k such that 3^k - k*2^k is prime.

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A270104 Numbers k such that 3^k + k*2^k is prime.

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A265505 Numbers n such that n*2^107 - 1 is prime.

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A265504 Numbers n such that n*2^2281 - 1 is prime.

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Magma

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A265503 Numbers n such that n*2^2203 - 1 is prime.

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Magma

Mathematica

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A265502 Numbers n such that n*2^1279 - 1 is prime.

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MATLAB

Magma

Mathematica

PARI

Extensions

A265499 Numbers n such that n*2^607 - 1 is prime.