A023264
Primes that remain prime through 2 iterations of function f(x) = 8x + 9.
Original entry on oeis.org
23, 43, 83, 109, 193, 379, 389, 569, 643, 659, 853, 1063, 1129, 1283, 1423, 1493, 1759, 1789, 1889, 2003, 2129, 2293, 2459, 2713, 2729, 2879, 2969, 3373, 3823, 4519, 4603, 4649, 4663, 4703, 4783, 4789, 5023, 5153, 5209, 5639, 5653, 5669, 5693, 5783, 6203
Offset: 1
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[n: n in [1..100000] | IsPrime(n) and IsPrime(8*n+9) and IsPrime(64*n+81)] // Vincenzo Librandi, Aug 04 2010
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Select[Prime[Range[1000]],AllTrue[Rest[NestList[8#+9&,#,2]],PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Sep 26 2016 *)
A153768
Numbers n such that n, 8n-9 and 8n+9 are primes.
Original entry on oeis.org
11, 29, 31, 109, 199, 251, 269, 379, 419, 521, 599, 601, 661, 881, 991, 1091, 1231, 1289, 1789, 1831, 1861, 1901, 1949, 2239, 2689, 2969, 3181, 3251, 3301, 3359, 3499, 3779, 3821, 4099, 4201, 4339, 4561, 4651, 4679, 4789, 4871, 5281, 5471, 5641, 5659
Offset: 1
For n=11, even 8n-9=79 and 8n+9=97 are primes, therefore 11 is in the sequence.
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[p: p in PrimesUpTo(6000) | IsPrime(8*p-9) and IsPrime(8*p+9)]; // Vincenzo Librandi, Apr 05 2013
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lst={}; Do[p=Prime[n]; If[PrimeQ[8*p-9]&&PrimeQ[8*p+9],AppendTo[lst,p]],{n,7!}]; lst (* Vladimir Joseph Stephan Orlovsky, Aug 16 2009 *)
Select[Prime[Range[6000]], PrimeQ[8 # - 9] && PrimeQ[8 # + 9] &] (* Vincenzo Librandi, Apr 05 2013 *)
Select[Prime[Range[800]],AllTrue[8#+{9,-9},PrimeQ]&] (* Harvey P. Dale, Apr 05 2023 *)
241 replaced by 251 and extended by
R. J. Mathar, Jan 07 2009
A023295
Primes that remain prime through 3 iterations of function f(x) = 8x + 9.
Original entry on oeis.org
23, 643, 2293, 5023, 5653, 9643, 10723, 11503, 12823, 15493, 18353, 18773, 28403, 32003, 32183, 41953, 42853, 45233, 49853, 50873, 52103, 53113, 54623, 56123, 76003, 80803, 84443, 86783, 88813, 89413, 92033, 95213, 96823, 97943, 100613, 115793
Offset: 1
A023351
Primes that remain prime through 5 iterations of function f(x) = 8x + 9.
Original entry on oeis.org
294793, 2586943, 5360623, 6351613, 7965743, 11141083, 11378453, 13458923, 14884823, 15585523, 18691633, 25387763, 29964293, 30766283, 32388253, 38647723, 40653433, 48716873, 48786593, 52628473, 54270533, 55507853, 56575633, 59103403
Offset: 1
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[n: n in [1..19000000] | IsPrime(n) and IsPrime(8*n+9) and IsPrime(64*n+81) and IsPrime(512*n+657) and IsPrime(4096*n+5265) and IsPrime(32768*n+42129)] // Vincenzo Librandi, Aug 05 2010
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prp5Q[n_]:=AllTrue[Rest[NestList[8#+9&,n,5]],PrimeQ]; Select[Prime[Range[3513000]],prp5Q] (* Harvey P. Dale, May 25 2024 *)
prp5Q2[n_] := AllTrue[NestList[8 # + 9 &, n, 5], PrimeQ]; Select[Range[23, 59120000, 70], prp5Q2] (* Faster than the first Mathematica program above. *) (* Harvey P. Dale, May 25 2024 *)
A153763
Numbers k >= 0 such that 8*k+9 is not prime.
Original entry on oeis.org
0, 2, 3, 5, 6, 7, 9, 12, 14, 15, 17, 18, 19, 20, 21, 22, 24, 25, 26, 27, 30, 32, 33, 35, 36, 37, 39, 40, 42, 44, 45, 46, 47, 48, 51, 52, 54, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 72, 75, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93
Offset: 1
Distribution of the terms in the following triangular array:
0;
*,2;
*,*,5;
*,*,*,9;
3,*,*,*,14;
*,7,*,*,*,20;
*,*,12,*,*,*,27;
*,*,*,18,*,*,*,35;
6,*,*,*,25,*,*,*,44;
*,12,*,*,*,33,*,*,*,54;
*,*,19,*,*,*,42,*,*,*,65; etc.
where * marks the non-integer values of (2*h*k + k + h - 4)/4 with h >= k >= 1. - _Vincenzo Librandi_, Jan 14 2013
Showing 1-5 of 5 results.
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