A157007
Numbers k such that 2^k + 27 is prime.
Original entry on oeis.org
1, 2, 4, 5, 8, 10, 13, 14, 16, 40, 41, 44, 86, 110, 125, 133, 134, 145, 154, 184, 194, 301, 308, 320, 685, 1001, 1066, 1496, 1633, 2005, 2864, 3241, 6286, 11585, 12854, 16514, 16540, 19246, 24538, 28705, 57644, 65366, 85276, 89113, 194854, 266680, 376790, 478088
Offset: 1
Edwin Dyke (ed.dyke(AT)btinternet.com), Feb 20 2009
For k = 1, 2^1 + 27 = 29.
For k = 2, 2^2 + 27 = 31.
For k = 4, 2^4 + 27 = 43.
Cf.
A019434 (primes 2^k+1),
A057732 (2^k+3),
A059242 (2^k+5),
A057195 (2^k+7),
A057196 (2^k+9),
A102633 (2^k+11),
A102634 (2^k+13),
A057197 (2^k+15),
A057200 (2^k+17),
A057221 (2^k+19),
A057201 (2^k+21),
A057203 (2^k+23),
A157006 (2^k+25), this sequence (2^k+27),
A156982 (2^k+29),
A247952 (2^k+31),
A247953 (2^k+33),
A220077 (2^k+35).
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[n: n in [0..1000] | IsPrime(2^n+27)]; // Vincenzo Librandi, Oct 05 2015
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Delete[Union[Table[If[PrimeQ[2^n + 27], n, 0], {n, 1, 2000}]], 1]
Select[Range[5000],PrimeQ[2^#+27]&] (* Harvey P. Dale, Mar 24 2011 *)
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for(n=1, 1e3, if(isprime(2^n+3^3), print1(n", "))) \\ Altug Alkan, Oct 04 2015
A144487
Primes of the form 2^k + 15.
Original entry on oeis.org
17, 19, 23, 31, 47, 79, 271, 1039, 2063, 4111, 32783, 65551, 4194319, 8388623, 67108879, 1073741839, 4294967311, 1099511627791, 4398046511119, 70368744177679, 2305843009213693967, 4722366482869645213711, 75557863725914323419151
Offset: 1
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[a: n in [1..100] | IsPrime(a) where a is 2^n+15]; // Vincenzo Librandi, Feb 23 2014
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Select[2^Range[0,200]+15,PrimeQ] (* Vladimir Joseph Stephan Orlovsky, Feb 03 2012 *)
Select[Table[2^n + 15, {n, 1, 300}], PrimeQ] (* Vincenzo Librandi, Feb 23 2014 *)
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{for(n=0, 72, if(isprime(k=2^n+15), print1(k, ",")))}
A247952
Numbers k such that 2^k + 31 is prime.
Original entry on oeis.org
4, 12, 36, 540, 844, 1192, 12136, 84280, 128356, 317464, 3018556
Offset: 1
Cf. Numbers k such that 2^k + d is prime: (0,1,2,4,8,16) for d=1;
A057732 (d=3),
A059242 (d=5),
A057195 (d=7),
A057196 (d=9),
A102633 (d=11),
A102634 (d=13),
A057197 (d=15),
A057200 (d=17),
A057221 (d=19),
A057201 (d=21),
A057203 (d=23),
A157006 (d=25),
A157007 (d=27),
A156982 (d=29), this sequence (d=31),
A247953 (d=33),
A220077 (d=35).
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[n: n in [0..2000]| IsPrime(2^n+31)];
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Select[Range[0,10000], PrimeQ[2^# + 31] &]
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is(n)=ispseudoprime(2^n+31) \\ Charles R Greathouse IV, May 22 2017
a(9)-a(10) (discovered by Lelio R Paula; see the Lifchitz link) added by
Robert Price, Oct 04 2015
A247953
Numbers k such that 2^k + 33 is prime.
Original entry on oeis.org
2, 3, 6, 11, 12, 14, 15, 20, 30, 60, 68, 75, 108, 116, 135, 206, 210, 410, 446, 558, 851, 1482, 1499, 2039, 2051, 4196, 7046, 7155, 8735, 10619, 18420, 20039, 46719, 75348, 179790, 203018, 434246
Offset: 1
Cf. Numbers k such that 2^k + d is prime: (0,1,2,4,8,16) for d=1;
A057732 (d=3),
A059242 (d=5),
A057195 (d=7),
A057196 (d=9),
A102633 (d=11),
A102634 (d=13),
A057197 (d=15),
A057200 (d=17),
A057221 (d=19),
A057201 (d=21),
A057203 (d=23),
A157006 (d=25),
A157007 (d=27),
A156982 (d=29),
A247952 (d=31), this sequence (d=33),
A220077 (d=35).
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/* The code gives only the terms up to 851: */ [n: n in [1..1400]| IsPrime( 2^n + 33 )];
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A247957:=n->`if`(isprime(2^n+33),n,NULL): seq(A247957(n), n=0..1000); # Wesley Ivan Hurt, Sep 28 2014
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Select[Range[10000], PrimeQ[2^# + 33] &]
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is(n)=ispseudoprime(2^n+33) \\ Charles R Greathouse IV, Feb 20 2017
A156982
Numbers k such that 2^k + 29 is prime.
Original entry on oeis.org
1, 3, 5, 7, 9, 13, 15, 17, 23, 27, 33, 37, 43, 63, 69, 73, 79, 89, 117, 127, 239, 395, 409, 465, 837, 2543, 10465, 10837, 17005, 19285, 24749, 26473, 29879, 49197, 56673, 67119, 67689, 71007, 109393, 156403, 158757, 181913, 190945, 207865, 222943, 419637
Offset: 1
Edwin Dyke (ed.dyke(AT)btinternet.com), Feb 20 2009
For k = 1, 2^1 + 29 = 31.
For k = 3, 2^3 + 29 = 37.
Cf.
A019434 (Fermat primes 2^(2^n)+1).
Cf.
A057732,
A059242,
A057195,
A057196,
A102633,
A102634,
A057197,
A057200,
A057221,
A057201,
A057203,
A157006,
A157007,
A247952,
A247953,
A220077.
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[n: n in [0..1000] | IsPrime(2^n+29)]; // Vincenzo Librandi, Oct 05 2015
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Delete[Union[Table[If[PrimeQ[2^n + 29], n, 0], {n, 1, 2600}]], 1]
Select[Range[500000], PrimeQ[2^#+29]&] (* Robert Price, Oct 04 2015 *)
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is(n)=ispseudoprime(2^n+29) \\ Charles R Greathouse IV, Jun 06 2017
A157006
Numbers k such that 2^k + 25 is prime.
Original entry on oeis.org
2, 4, 6, 8, 10, 20, 22, 34, 70, 92, 112, 118, 236, 250, 378, 438, 570, 654, 800, 1636, 2848, 4948, 5670, 6772, 7494, 8006, 9056, 11038, 16268, 21416, 21738, 33370, 78706, 112130, 126446, 164046, 219250, 236432, 368048, 524154, 530810, 640854, 699740, 746302, 754038, 754376, 931976, 989562
Offset: 1
Edwin Dyke (ed.dyke(AT)btinternet.com), Feb 20 2009
For k = 2, 2^2 + 25 = 29.
For k = 4, 2^4 + 25 = 41.
For k = 6, 2^6 + 25 = 89.
Cf.
A019434 (primes 2^k+1),
A057732 (2^k+3),
A059242 (2^k+5),
A057195 (2^k+7),
A057196 (2^k+9),
A102633 (2^k+11),
A102634 (2^k+13),
A057197 (2^k+15),
A057200 (2^k+17),
A057221 (2^k+19),
A057201 (2^k+21),
A057203 (2^k+23), this sequence (2^k+25),
A157007 (2^k+27),
A156982 (2^k+29),
A247952 (2^k+31),
A247953 (2^k+33),
A220077 (2^k+35).
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[n: n in [1..1000] | IsPrime(2^n+25)]; // Vincenzo Librandi, Aug 07 2016
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Delete[Union[Table[If[PrimeQ[2^n + 25], n, 0], {n, 1, 1000}]], 1]
Select[Range[0, 10000], PrimeQ[2^# + 25] &] (* Vincenzo Librandi, Aug 07 2016 *)
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is(n)=ispseudoprime(2^n+5^2) \\ Charles R Greathouse IV, Feb 20 2017
A220077
Numbers k such that 2^k + 35 is prime.
Original entry on oeis.org
1, 3, 5, 7, 9, 11, 15, 25, 33, 57, 117, 133, 189, 195, 263, 273, 287, 509, 693, 1087, 1145, 1159, 1845, 2743, 3275, 12223, 26263, 31425, 44359, 48003, 49251, 62557, 113877, 114507, 132865, 165789, 192549, 348437, 426043, 436365, 471043, 480417
Offset: 1
Cf. Numbers k such that 2^k + d is prime: (0,1,2,4,8,16) for d=1;
A057732 (d=3),
A059242 (d=5),
A057195 (d=7),
A057196 (d=9),
A102633 (d=11),
A102634 (d=13),
A057197 (d=15),
A057200 (d=17),
A057221 (d=19),
A057201 (d=21),
A057203 (d=23),
A157006 (d=25),
A157007 (d=27),
A156982 (d=29),
A247952 (d=31),
A247953 (d=33), this sequence (d=35).
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Select[Range[5000],PrimeQ[2^# + 35] &]
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for(n=1, 10^30, if (isprime(2^n + 35), print1(n", "))); \\ Altug Alkan, Oct 05 2015
132865, 165789, 192549, 348437 discovered by Lelio R Paula confirmed as a(35)-a(38) by
Robert Price, Oct 05 2015
A144670
Triangle read by rows where T(m,n)=2mn+m+n-7.
Original entry on oeis.org
-3, 0, 5, 3, 10, 17, 6, 15, 24, 33, 9, 20, 31, 42, 53, 12, 25, 38, 51, 64, 77, 15, 30, 45, 60, 75, 90, 105, 18, 35, 52, 69, 86, 103, 120, 137, 21, 40, 59, 78, 97, 116, 135, 154, 173, 24, 45, 66, 87, 108, 129, 150, 171, 192, 213, 27, 50, 73, 96, 119, 142, 165, 188, 211, 234, 257
Offset: 1
Triangle begins:
-3;
0, 5;
3, 10, 17;
6, 15, 24, 33;
9, 20, 31, 42, 53;
12, 25, 38, 51, 64, 77;
15, 30, 45, 60, 75, 90, 105;
18, 35, 52, 69, 86, 103, 120, 137;
21, 40, 59, 78, 97, 116, 135, 154, 173;
24, 45, 66, 87, 108, 129, 150, 171, 192, 213;
= = = = = = = =
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[2*n*k + n + k -7: k in [1..n], n in [1..12]]; // Vincenzo Librandi, Oct 15 2012
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t[n_,k_]:=2 n*k+n+k-7; Table[t[n, k], {n, 12}, {k, n}] // Flatten (* Vincenzo Librandi, Oct 15 2012 *)
A175234
Primes p such that 2^p+15 is also prime.
Original entry on oeis.org
2, 3, 5, 11, 23, 61
Offset: 1
For p=2, 2^2+15=19; p=3, 2^3+15=23; p=5, 2^5+15=47.
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[p: p in PrimesUpTo(6000) | IsPrime(2^p+15) ]
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Select[Prime[Range[1000]],PrimeQ[2^#+15]&] (* Harvey P. Dale, Apr 13 2014 *)
A211486
Primes of the form 5+3*2^k.
Original entry on oeis.org
11, 17, 29, 53, 101, 197, 389, 773, 49157, 196613, 1572869, 12582917, 50331653, 402653189, 1610612741, 12884901893, 824633720837, 54043195528445957, 432345564227567621, 3458764513820540933, 226673591177742970257413, 59421121885698253195157962757
Offset: 1
Cf.
A057913 (n such that 3*2^n + 5 is prime).
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[ a: n in [0..250] | IsPrime(a) where a is 5+3*2^n ];
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Select[5+2^Range[0,2000]*3,PrimeQ]
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{for(n=0, 80, if(isprime(k=5+3*2^n), print1(k, ", ")))}
Comments