A097338 -id:A097338 - cp's OEIS frontend

A101448 Nonnegative numbers k such that 2k + 11 is prime.

0, 1, 3, 4, 6, 9, 10, 13, 15, 16, 18, 21, 24, 25, 28, 30, 31, 34, 36, 39, 43, 45, 46, 48, 49, 51, 58, 60, 63, 64, 69, 70, 73, 76, 78, 81, 84, 85, 90, 91, 93, 94, 100, 106, 108, 109, 111, 114, 115, 120, 123, 126, 129, 130, 133, 135, 136, 141, 148, 150, 151, 153, 160, 163

Offset: 1

Parthasarathy Nambi, Jan 24 2005

2 is the smallest single-digit prime and 11 is the smallest two-digit prime.

			If n=1, then 2*1 + 11 = 13 (prime).
If n=49, then 2*49 + 11 = 109 (prime).
If n=69, then 2*69 + 11 = 149 (prime).

Shawn A. Broyles, Table of n, a(n) for n = 1..1000

Cf. A101123, A101086.
Numbers n such that 2n+k is prime: A005097 (k=1), A067076 (k=3), A089038 (k=5), A105760 (k=7), A155722 (k=9), this seq (k=11), A153081 (k=13), A089559 (k=15), A173059 (k=17), A153143 (k=19).
Numbers n such that 2n-k is prime: A006254 (k=1), A098090 (k=3), A089253 (k=5), A089192 (k=7), A097069 (k=9), A097338 (k=11), A097363 (k=13), A097480 (k=15), A098605 (k=17), A097932 (k=19).

Filtered([0..200], k-> IsPrime(2*k+11) ); # G. C. Greubel, May 21 2019

[n: n in [0..200] | IsPrime(2*n+11)]; // Vincenzo Librandi, Nov 17 2010

select(k-> isprime(11+2*k), [$0..200])[];  # Alois P. Heinz, Jun 02 2022

Select[Range[0, 200], PrimeQ[2# + 11] &] (* Stefan Steinerberger, Feb 28 2006 *)

is(n)=isprime(2*n+11) \\ Charles R Greathouse IV, Apr 29 2015

[n for n in (0..200) if is_prime(2*n+11) ] # G. C. Greubel, May 21 2019

More terms from Stefan Steinerberger, Feb 28 2006

Definition clarified by Zak Seidov, Jul 11 2014

A097069 Positive integers n such that 2n - 9 is prime.

Original entry on oeis.org

6, 7, 8, 10, 11, 13, 14, 16, 19, 20, 23, 25, 26, 28, 31, 34, 35, 38, 40, 41, 44, 46, 49, 53, 55, 56, 58, 59, 61, 68, 70, 73, 74, 79, 80, 83, 86, 88, 91, 94, 95, 100, 101, 103, 104, 110, 116, 118, 119, 121, 124, 125, 130, 133, 136, 139, 140, 143, 145, 146, 151, 158, 160

Offset: 1

Douglas Winston (douglas.winston(AT)srupc.com), Sep 15 2004

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A000040, A086801.
Numbers n such that 2n+k is prime: A005097 (k=1), A067076 (k=3), A089038 (k=5), A105760 (k=7), A155722 (k=9), A101448 (k=11), A153081 (k=13), A089559 (k=15), A173059 (k=17), A153143 (k=19).
Numbers n such that 2n-k is prime: A006254 (k=1), A098090 (k=3), A089253 (k=5), A089192 (k=7), this seq(k=9), A097338 (k=11), A097363 (k=13), A097480 (k=15), A098605 (k=17), A097932 (k=19).

[n: n in [6..160] | IsPrime(2*n-9)];  // Bruno Berselli, Mar 05 2011

(Prime[Range[2,100]]+9)/2 (* Vladimir Joseph Stephan Orlovsky, Feb 08 2010 *)
Select[Range[4, 200], PrimeQ[2 # - 9] &] (* Vincenzo Librandi, Oct 16 2012 *)

is(n)=isprime(2*n-9) \\ Charles R Greathouse IV, Apr 28 2015

Half of p+9 where p is a prime greater than 2.

A097932 Positive integers n such that 2n-19 is prime.

Original entry on oeis.org

11, 12, 13, 15, 16, 18, 19, 21, 24, 25, 28, 30, 31, 33, 36, 39, 40, 43, 45, 46, 49, 51, 54, 58, 60, 61, 63, 64, 66, 73, 75, 78, 79, 84, 85, 88, 91, 93, 96, 99, 100, 105, 106, 108, 109, 115, 121, 123, 124, 126, 129, 130, 135, 138, 141, 144, 145, 148, 150, 151, 156, 163

Offset: 1

Douglas Winston (douglas.winston(AT)srupc.com), Sep 21 2004

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A000040.
Numbers n such that 2n+k is prime: A005097 (k=1), A067076 (k=3), A089038 (k=5), A105760 (k=7), A155722 (k=9), A101448 (k=11), A153081 (k=13), A089559 (k=15), A173059 (k=17), A153143 (k=19).
Numbers n such that 2n-k is prime: A006254 (k=1), A098090 (k=3), A089253 (k=5), A089192 (k=7), A097069 (k=9), A097338 (k=11), A097363 (k=13), A097480 (k=15), A098605 (k=17), this sequence (k=19).

(Prime[Range[2,100]]+19)/2 (* Vladimir Joseph Stephan Orlovsky, Feb 08 2010 *)
Select[Range[10,200],PrimeQ[2#-19]&] (* Harvey P. Dale, May 08 2017 *)

Half of p+19 where p is a prime greater than 2.

A153081 Nonnegative numbers k such that 2k + 13 is prime.

Original entry on oeis.org

0, 2, 3, 5, 8, 9, 12, 14, 15, 17, 20, 23, 24, 27, 29, 30, 33, 35, 38, 42, 44, 45, 47, 48, 50, 57, 59, 62, 63, 68, 69, 72, 75, 77, 80, 83, 84, 89, 90, 92, 93, 99, 105, 107, 108, 110, 113, 114, 119, 122, 125, 128, 129, 132, 134, 135, 140, 147, 149, 150, 152, 159, 162, 167

Offset: 1

Vincenzo Librandi, Dec 18 2008

Or, (p-13)/2 for primes p >= 13.
a(n) = (A000040(n+5) - 13)/2.
a(n) = A005097(n+4) - 6.
a(n) = A067076(n+4) - 5.
a(n) = A089038(n+3) - 4.
a(n) = A105760(n+2) - 3.
a(n) = A101448(n+1) - 1.
a(n) = A089559(n-1) + 1 for n > 1.

			For k = 7, 2*k+13 = 27 is not prime, so 7 is not in the sequence;
for k = 8, 2*k+13 = 29 is prime, so 8 is in the sequence.

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A000040 (prime numbers).
Numbers n such that 2n+k is prime: A005097 (k=1), A067076 (k=3), A089038 (k=5), A105760 (k=7), A155722 (k=9), A101448 (k=11), this seq (k=13), A089559 (k=15), A173059 (k=17), A153143 (k=19).
Numbers n such that 2n-k is prime: A006254 (k=1), A098090 (k=3), A089253 (k=5), A089192 (k=7), A097069 (k=9), A097338 (k=11), A097363 (k=13), A097480 (k=15), A098605 (k=17), A097932 (k=19).

Filtered([0..200], k-> IsPrime(2*k+13) ); # G. C. Greubel, May 22 2019

[ n: n in [0..200] | IsPrime(2*n+13) ];

(Prime[Range[6,100]]-13)/2 (* Vladimir Joseph Stephan Orlovsky, Feb 08 2010 *)
Select[Range[0,200],PrimeQ[2#+13]&] (* Harvey P. Dale, Mar 02 2015 *)

is(n)=isprime(2*n+13) \\ Charles R Greathouse IV, Jul 12 2016

[n for n in (0..200) if is_prime(2*n+13) ] # G. C. Greubel, May 22 2019

Edited and extended by Klaus Brockhaus, Dec 22 2008

Definition clarified by Zak Seidov, Jul 11 2014

A097480 Positive integers n such that 2n-15 is prime.

Original entry on oeis.org

9, 10, 11, 13, 14, 16, 17, 19, 22, 23, 26, 28, 29, 31, 34, 37, 38, 41, 43, 44, 47, 49, 52, 56, 58, 59, 61, 62, 64, 71, 73, 76, 77, 82, 83, 86, 89, 91, 94, 97, 98, 103, 104, 106, 107, 113, 119, 121, 122, 124, 127, 128, 133, 136, 139, 142, 143, 146, 148, 149, 154, 161, 163

Offset: 1

Douglas Winston (douglas.winston(AT)srupc.com), Sep 19 2004

Shawn A. Broyles, Table of n, a(n) for n = 1..1000

Cf. A000040, A098602, A098603.
Numbers n such that 2n+k is prime: A005097 (k=1), A067076 (k=3), A089038 (k=5), A105760 (k=7), A155722 (k=9), A101448 (k=11), A153081 (k=13), A089559 (k=15), A173059 (k=17), A153143 (k=19).
Numbers n such that 2n-k is prime: A006254 (k=1), A098090 (k=3), A089253 (k=5), A089192 (k=7), A097069 (k=9), A097338 (k=11), A097363 (k=13), this sequence (k=15), A098605 (k=17), A097932 (k=19).

(Prime[Range[2,100]]+15)/2 (* Vladimir Joseph Stephan Orlovsky, Feb 08 2010 *)
Select[Range[9,200],PrimeQ[2#-15]&] (* Harvey P. Dale, Apr 04 2021 *)

is(n)=isprime(2*n-15) \\ Charles R Greathouse IV, Jul 12 2016

Half of p+15 where p is a prime greater than 2.

A098605 Positive integers n such that 2n - 17 is prime.

Original entry on oeis.org

10, 11, 12, 14, 15, 17, 18, 20, 23, 24, 27, 29, 30, 32, 35, 38, 39, 42, 44, 45, 48, 50, 53, 57, 59, 60, 62, 63, 65, 72, 74, 77, 78, 83, 84, 87, 90, 92, 95, 98, 99, 104, 105, 107, 108, 114, 120, 122, 123, 125, 128, 129, 134, 137, 140, 143, 144, 147, 149, 150, 155, 162

Offset: 1

Douglas Winston (douglas.winston(AT)srupc.com), Sep 20 2004

Shawn A. Broyles, Table of n, a(n) for n = 1..1000

Cf. A000040, A098602, A098603.
Numbers n such that 2n+k is prime: A005097 (k=1), A067076 (k=3), A089038 (k=5), A105760 (k=7), A155722 (k=9), A101448 (k=11), A153081 (k=13), A089559 (k=15), A173059 (k=17), A153143 (k=19).
Numbers n such that 2n-k is prime: A006254 (k=1), A098090 (k=3), A089253 (k=5), A089192 (k=7), A097069 (k=9), A097338 (k=11), A097363 (k=13), A097480 (k=15), this sequence (k=17), A097932 (k=19).

(Prime[Range[2,100]]+17)/2 (* Vladimir Joseph Stephan Orlovsky, Feb 08 2010 *)

is(n)=isprime(2*n-17) \\ Charles R Greathouse IV, Jul 12 2016

Half of p+17 where p is a prime greater than 2.

A173059 Nonnegative numbers k such that 2*k + 17 is prime.

Original entry on oeis.org

0, 1, 3, 6, 7, 10, 12, 13, 15, 18, 21, 22, 25, 27, 28, 31, 33, 36, 40, 42, 43, 45, 46, 48, 55, 57, 60, 61, 66, 67, 70, 73, 75, 78, 81, 82, 87, 88, 90, 91, 97, 103, 105, 106, 108, 111, 112, 117, 120, 123, 126, 127, 130, 132, 133, 138, 145, 147, 148, 150, 157, 160, 165

Offset: 1

Vladimir Joseph Stephan Orlovsky, Feb 08 2010

Shawn A. Broyles, Table of n, a(n) for n = 1..1000

Numbers n such that 2n+k is prime: A005097 (k=1), A067076 (k=3), A089038 (k=5), A105760 (k=7), A155722 (k=9), A101448 (k=11), A153081 (k=13), A089559 (k=15), this seq (k=17), A153143 (k=19).

Numbers n such that 2n-k is prime: A006254 (k=1), A098090 (k=3), A089253 (k=5), A089192 (k=7), A097069 (k=9), A097338 (k=11), A097363 (k=13), A097480 (k=15), A098605 (k=17), A097932 (k=19).

Filtered([0..200], k-> IsPrime(2*k+17) ); # G. C. Greubel, May 22 2019

[n: n in [0..200] | IsPrime(2*n+17) ]; // G. C. Greubel, May 22 2019

Mathematica
```
(Prime[Range[7,100]]-17)/2
```

is(n)=isprime(2*n+17) \\ Charles R Greathouse IV, Feb 17 2017

[n for n in (0..200) if is_prime(2*n+17) ] # G. C. Greubel, May 22 2019

Definition clarified by Zak Seidov, Jul 11 2014

A097363 Positive integers n such that 2n-13 is prime.

Original entry on oeis.org

8, 9, 10, 12, 13, 15, 16, 18, 21, 22, 25, 27, 28, 30, 33, 36, 37, 40, 42, 43, 46, 48, 51, 55, 57, 58, 60, 61, 63, 70, 72, 75, 76, 81, 82, 85, 88, 90, 93, 96, 97, 102, 103, 105, 106, 112, 118, 120, 121, 123, 126, 127, 132, 135, 138, 141, 142, 145, 147, 148, 153, 160, 162

Offset: 1

Douglas Winston (douglas.winston(AT)srupc.com), Sep 18 2004

Shawn A. Broyles, Table of n, a(n) for n = 1..1000

Cf. A000040, A098602.
Numbers n such that 2n+k is prime: A005097 (k=1), A067076 (k=3), A089038 (k=5), A105760 (k=7), A155722 (k=9), A101448 (k=11), A153081 (k=13), A089559 (k=15), A173059 (k=17), A153143 (k=19).
Numbers n such that 2n-k is prime: A006254 (k=1), A098090 (k=3), A089253 (k=5), A089192 (k=7), A097069 (k=9), A097338 (k=11), this sequence (k=13), A097480 (k=15), A098605 (k=17), A097932 (k=19).

(Prime[Range[2,100]]+13)/2 (* Vladimir Joseph Stephan Orlovsky, Feb 08 2010 *)
Select[Range[8,200],PrimeQ[2#-13]&] (* Harvey P. Dale, Apr 26 2013 *)

Half of p+13 where p is a prime greater than 2.

A153045 Numbers k such that 2*k-11 is not a prime.

Original entry on oeis.org

10, 13, 16, 18, 19, 22, 23, 25, 28, 30, 31, 33, 34, 37, 38, 40, 43, 44, 46, 48, 49, 51, 52, 53, 55, 58, 61, 63, 64, 65, 66, 67, 68, 70, 72, 73, 76, 77, 78, 79, 82, 83, 85, 86, 88, 90, 91, 93, 94, 97, 98, 99, 100, 103, 106, 107, 108, 109, 110, 112, 113, 114

Offset: 1

Vincenzo Librandi, Dec 17 2008

The terms are the values of 2*h*k + k + h + 6, where h and k are positive integers. - Vincenzo Librandi, Jan 19 2013

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A097338, A153043, A163652, A104275.

[n: n in [7..120] | not IsPrime(2*n - 11)]; // Vincenzo Librandi, Oct 11 2012

Select[Range[10,200], !PrimeQ[2*#-11]&] (* Vladimir Joseph Stephan Orlovsky, Feb 09 2012 *)

from sympy import isprime
def ok(n): return n > 6 and not isprime(2*n-11)
print(list(filter(ok, range(115)))) # Michael S. Branicky, Oct 13 2021

a(n) = 5+A104275(n+1). [R. J. Mathar, Oct 22 2009]

A118469 Triangle read by rows: a(n,m) = If(n = 1, then 1, else Prime(n) - 1 + Sum_{k=n..m} (Prime(k + 1) - Prime(k))/2 ).

Original entry on oeis.org

1, 1, 3, 1, 4, 5, 1, 6, 7, 8, 1, 7, 8, 9, 11, 1, 9, 10, 11, 13, 14, 1, 10, 11, 12, 14, 15, 17, 1, 12, 13, 14, 16, 17, 19, 20, 1, 15, 16, 17, 19, 20, 22, 23, 25, 1, 16, 17, 18, 20, 21, 23, 24, 26, 29, 1, 19, 20, 21, 23, 24, 26, 27, 29, 32, 33, 1, 21, 22, 23, 25, 26, 28, 29, 31, 34, 35

Offset: 1

Roger L. Bagula, May 04 2006

An improved triangular Goldbach sequence in which the gap sum is taken from a start at n.

			1
1, 3
1, 4, 5
1, 6, 7, 8
1, 7, 8, 9, 11
1, 9, 10, 11, 13, 14
1, 10, 11, 12, 14, 15, 17
1, 12, 13, 14, 16, 17, 19, 20
1, 15, 16, 17, 19, 20, 22, 23, 25
1, 16, 17, 18, 20, 21, 23, 24, 26, 29

Main diagonal: A078444, 2nd diagonal: A073273.

Columns 1-8: A000012, A006254, A098090, A089253, A097069, A097338, A097480, A098605.

t[n_, m_] := If[n == 1, 1, Prime[n] + Sum[(Prime[k + 1] - Prime[k])/2, {k, n, m}] - 1]; Table[ t[n, m], {m, 11}, {n, m}] // Flatten

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A101448 Nonnegative numbers k such that 2k + 11 is prime.

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A097069 Positive integers n such that 2n - 9 is prime.

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A097932 Positive integers n such that 2n-19 is prime.

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A153081 Nonnegative numbers k such that 2k + 13 is prime.

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A097480 Positive integers n such that 2n-15 is prime.

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A098605 Positive integers n such that 2n - 17 is prime.

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A173059 Nonnegative numbers k such that 2*k + 17 is prime.

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