A139487
Numbers k such that 8k + 7 is prime.
Original entry on oeis.org
0, 2, 3, 5, 8, 9, 12, 15, 18, 20, 23, 24, 27, 29, 32, 33, 38, 44, 45, 47, 53, 54, 57, 59, 60, 62, 74, 75, 78, 80, 89, 90, 92, 93, 102, 104, 107, 110, 113, 114, 120, 122, 123, 128, 129, 132, 135, 137, 143, 152, 153, 159, 162, 164, 165, 170, 174, 177, 179, 180, 183, 185
Offset: 1
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[n: n in [0..200] | IsPrime(8*n+7)]; // Vincenzo Librandi, Jun 25 2014
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a = {}; Do[If[PrimeQ[8 n + 7], AppendTo[a, n]], {n, 0, 300}]; a
Select[Range[0,200],PrimeQ[8#+7]&] (* Harvey P. Dale, Oct 10 2012 *)
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is(n)=isprime(8*n+7) \\ Charles R Greathouse IV, Feb 17 2017
A023229
Primes p such that 8*p + 3 is also prime.
Original entry on oeis.org
2, 5, 7, 13, 17, 31, 41, 43, 47, 61, 71, 73, 101, 103, 107, 113, 127, 131, 157, 163, 181, 191, 197, 223, 233, 241, 251, 281, 283, 293, 307, 317, 337, 367, 383, 421, 433, 443, 457, 461, 467, 491, 503, 563, 631, 643, 647, 653, 673, 677, 691, 733, 751, 761, 787, 797, 811
Offset: 1
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[n: n in PrimesUpTo(1000) | IsPrime(8*n+3)]; // Vincenzo Librandi, Nov 20 2010
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a := proc (n) if isprime(n) = true and isprime(8*n+3) = true then n else end if end proc: seq(a(n), n = 1 .. 900); # Emeric Deutsch, Dec 26 2008
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Select[Prime@Range@500, PrimeQ[8 # + 3] &] (* Vincenzo Librandi, May 19 2014 *)
A023261
Primes that remain prime through 2 iterations of function f(x) = 8x + 3.
Original entry on oeis.org
5, 13, 31, 61, 101, 103, 163, 191, 233, 241, 251, 433, 461, 643, 751, 761, 821, 863, 983, 1021, 1153, 1193, 1283, 1291, 1531, 1543, 1861, 2281, 2543, 2903, 2953, 3271, 3373, 3673, 3701, 3733, 3793, 3923, 4003, 4241, 4283, 4751, 5333, 5581, 5711, 5801, 5813
Offset: 1
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[n: n in [1..100000] | IsPrime(n) and IsPrime(8*n+3) and IsPrime(64*n+27)] // Vincenzo Librandi, Aug 04 2010
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Select[Prime[Range[800]],AllTrue[Rest[NestList[8#+3&,#,2]],PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Aug 12 2017 *)
A023348
Primes that remain prime through 5 iterations of function f(x) = 8x + 3.
Original entry on oeis.org
774791, 924731, 4593221, 5181641, 9905521, 11523361, 11755831, 12253321, 14078711, 14545331, 14928791, 18523361, 18686531, 24169001, 25614361, 26221051, 26834461, 30970201, 33446521, 40051021, 42888191, 43703201, 47528561, 48653951
Offset: 1
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[n: n in [1..19000000] | IsPrime(n) and IsPrime(8*n+3) and IsPrime(64*n+27) and IsPrime(512*n+219) and IsPrime(4096*n+1755) and IsPrime(32768*n+14043)] // Vincenzo Librandi, Aug 05 2010
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n5Q[n_]:=And@@PrimeQ/@NestList[8#+3&,n,5]; Select[Prime[Range[ 3000000]], n5Q] (* Harvey P. Dale, Sep 03 2013 *)
A123978
Numbers k for which 8*k+1, 8*k+3 and 8*k+7 are primes.
Original entry on oeis.org
2, 5, 80, 107, 110, 185, 260, 332, 500, 1067, 1307, 1472, 1625, 1760, 1790, 1955, 2255, 2612, 2627, 2672, 2882, 2945, 3197, 3335, 3467, 3965, 4007, 4037, 4040, 4202, 4355, 4880, 5147, 5252, 5525, 6242, 6812, 6917, 6977, 7430, 7787, 8192, 8612, 8657, 8720
Offset: 1
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Select[Range[10^4], And @@ PrimeQ /@ ({1, 3, 7} + 8#) &] (* Ray Chandler, Nov 05 2006 *)
A123980
Numbers k for which 8*k+1, 8*k+5 and 8*k+7 are primes.
Original entry on oeis.org
12, 24, 57, 162, 234, 249, 267, 297, 432, 519, 564, 717, 969, 984, 1167, 1179, 1389, 1734, 2007, 2364, 2427, 2544, 2664, 2769, 2784, 3582, 3627, 3819, 3897, 4089, 4287, 5244, 5307, 5337, 5472, 5577, 5667, 5727, 5967, 6084, 6102, 6399, 6522, 6822, 6987
Offset: 1
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Select[Range[7000], And @@ PrimeQ /@ ({1, 5, 7} + 8#) &] (* Ray Chandler, Nov 05 2006 *)
A123983
Numbers k for which 8*k+1, 8*k+5, 8*k+7 and 8*k+11 are primes.
Original entry on oeis.org
12, 57, 162, 249, 432, 564, 984, 1734, 2007, 2427, 2664, 2784, 3627, 5307, 5472, 5727, 6399, 7614, 11082, 11547, 11607, 11694, 14127, 14274, 14484, 14862, 15117, 17049, 19104, 19422, 20577, 25677, 27612, 27714, 28152, 29307, 32232, 34602, 35592
Offset: 1
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isA123983 := proc(n) RETURN( isprime(8*n+1) and isprime(8*n+5) and isprime(8*n+7) and isprime(8*n+11) ) ; end: for n from 1 to 7000 do if isA123983(n) then printf("%d,",n) ; fi ; od ; # R. J. Mathar, Nov 06 2006
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Select[Range[37000], And @@ PrimeQ /@ ({1, 5, 7, 11} + 8#) &] (* Ray Chandler, Nov 05 2006 *)
A153236
Numbers n such that 8*n + 3 is not prime.
Original entry on oeis.org
3, 4, 6, 9, 11, 12, 14, 15, 18, 19, 21, 23, 24, 25, 27, 29, 30, 32, 33, 34, 36, 37, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 53, 54, 56, 57, 59, 60, 63, 64, 66, 67, 69, 72, 74, 75, 76, 78, 79, 81, 83, 84, 87, 88, 89, 90, 91, 93, 94, 95, 96, 97
Offset: 1
Distribution of the terms in the following triangular array:
*;
*,*;
*,4,*;
3,*,*,*;
*,*,*,12,*;
*,*,11,*,*,*;
*,9,*,*,*,24,*;
6,*,*,*,23,*,*,*;
*,*,*,21,*,*,*,40,*;
*,*,18,*,*,*,39,*,*,*;
*,14,*,*,*,37,*,*,*,60,*;
9,*,*,*,34,*,*,*,59,*,*,*; etc.
where * marks the non-integer values of (2*h*k + k + h - 1)/4 with h >= k >= 1. - _Vincenzo Librandi_, Jan 15 2013
A199427
Numbers n such that 4n+1 and 8n+3 are prime.
Original entry on oeis.org
1, 7, 10, 13, 22, 28, 43, 58, 70, 73, 127, 148, 160, 163, 190, 202, 238, 253, 262, 307, 322, 352, 370, 400, 433, 472, 475, 493, 517, 532, 535, 568, 598, 637, 673, 685, 688, 742, 832, 847, 853, 862, 898, 940, 955, 1018, 1087, 1093, 1102, 1120, 1183, 1198, 1270
Offset: 1
For n = 1, both 11 and 5 are primes, hence 2 is a primitive root of 11.
- Albert H. Beiler: Recreations in the theory of numbers. New York: Dover, (2nd ed.) 1966, p. 102, nr. 4.
Showing 1-9 of 9 results.
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