A153762
Numbers k such that 8k + 9 is prime.
Original entry on oeis.org
1, 4, 8, 10, 11, 13, 16, 23, 28, 29, 31, 34, 38, 41, 43, 49, 50, 53, 55, 56, 64, 70, 71, 73, 74, 76, 79, 83, 94, 95, 100, 106, 109, 115, 116, 118, 121, 125, 128, 130, 136, 140, 143, 148, 149, 151, 155, 160, 161, 164, 169, 175, 178, 184, 185, 193, 199, 200, 206, 211
Offset: 1
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 *)
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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