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

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

1,2

Comments

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.

Links

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

Example

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.

Mathematica

(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 *)

Prog

(Magma) [ n: n in [0..200] | IsPrime(2*n+13) ];
(PARI) is(n)=isprime(2*n+13) \\ Charles R Greathouse IV, Jul 12 2016
(Sage) [n for n in (0..200) if is_prime(2*n+13) ] # G. C. Greubel, May 22 2019
(GAP) Filtered([0..200], k-> IsPrime(2*k+13) ) # G. C. Greubel, May 22 2019

Crossrefs

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).

Sequence in context: A013634 A133484 A181155 * A190841 A095952 A286492

Adjacent sequences: A153078 A153079 A153080 * A153082 A153083 A153084

Keyword

easy,nonn

Author

Vincenzo Librandi, Dec 18 2008

Extensions

Edited and extended by Klaus Brockhaus, Dec 22 2008

Definition clarified by Zak Seidov, Jul 11 2014

Status

approved