A098090 Numbers k such that 2k-3 is prime.

3, 4, 5, 7, 8, 10, 11, 13, 16, 17, 20, 22, 23, 25, 28, 31, 32, 35, 37, 38, 41, 43, 46, 50, 52, 53, 55, 56, 58, 65, 67, 70, 71, 76, 77, 80, 83, 85, 88, 91, 92, 97, 98, 100, 101, 107, 113, 115, 116, 118, 121, 122, 127, 130, 133, 136, 137, 140, 142, 143, 148, 155, 157, 158

Offset: 1

Author

Douglas Winston (douglas.winston(AT)srupc.com), Sep 14 2004

Keywords

• easy
• nonn

Comments

Supersequence of A063908.

Left edge of the triangle in A065305. - Reinhard Zumkeller, Jan 30 2012

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A085090, 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), this sequence (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).

Programs

GAP

Filtered([1..200], k-> IsPrime(2*k-3) ); # G. C. Greubel, May 21 2019

Magma

[ n: n in [1..200] | IsPrime(2*n-3) ]; // Vincenzo Librandi, Dec 26 2010

Mathematica

(Prime[Range[2,100]]+3)/2 (* Vladimir Joseph Stephan Orlovsky, Feb 08 2010 *)
Select[Range[200],PrimeQ[2#-3]&] (* Harvey P. Dale, Mar 05 2022 *)

PARI

is(n)=isprime(2*n-3) \\ Charles R Greathouse IV, Feb 17 2017

Sage

[n for n in (1..200) if is_prime(2*n-3) ] # G. C. Greubel, May 21 2019

Formula

Half of p + 3, where p is a prime greater than 2.

A122845(a(n), 3) = 3; a(n) = A113935(n+1)/2. - Reinhard Zumkeller, Sep 14 2006