A048198 -id:A048198 - cp's OEIS frontend

A321972 Numbers k for which A048198(k)=3.

1, 2, 4, 7, 10, 11, 23, 28, 31, 35, 46, 86, 88, 109, 128, 130, 143, 145, 149, 161, 187, 200, 214, 224, 227, 238, 266, 269, 271, 280, 346, 353, 385, 392, 413, 452, 464, 479, 497, 523, 544, 548, 565, 574, 620, 655, 683, 721, 788, 809, 829, 854, 901, 928, 934, 1027, 1043, 1046, 1178, 1183, 1204

Offset: 1

Robert Israel, Nov 22 2018

nonn

Numbers k for which three of 10*k-3, 10*k-1, 10*k+1, 10*k+3 are prime.
Note: they can't all be prime because at least one must be divisible by 3.
No terms are divisible by 3.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A048198.

filter:= n -> nops(select(isprime,[10*n-3,10*n-1,10*n+1,10*n+3]))=3:
select(filter, [$1..1000]); # Robert Israel, Nov 22 2018

Select[Range[1204], AllTrue[Rest@Sort@PrimeQ[10 # + {-3, -1, 1, 3}], TrueQ] &] (* Amiram Eldar, Nov 22 2018 *)

A048199 Distance of primes to next odd multiple of 5 (where n mod 10 = 5).

Original entry on oeis.org

3, 2, 0, 8, 4, 2, 8, 6, 2, 6, 4, 8, 4, 2, 8, 2, 6, 4, 8, 4, 2, 6, 2, 6, 8, 4, 2, 8, 6, 2, 8, 4, 8, 6, 6, 4, 8, 2, 8, 2, 6, 4, 4, 2, 8, 6, 4, 2, 8, 6, 2, 6, 4, 4, 8, 2, 6, 4, 8, 4, 2, 2, 8, 4, 2, 8, 4, 8, 8, 6, 2, 6, 8, 2, 6, 2, 6, 8, 4, 6, 6, 4, 4, 2, 6, 2, 6, 8, 4, 2, 8, 6, 8, 4, 6, 2, 6, 4, 2, 4, 8, 8, 2, 6, 4

Offset: 1

Enoch Haga

			Take first prime 2, subtract from 5: 5-2=3, distance to 5; take 5-5 = 0; or 4th term, 15-7=8. Sequence may be converted to distance to nearest value of n (absolute value, where n mod 10 = 5) by changing all 8's to 2's and all 6's to 4's.

Cf. A048198, A007652.

a(n) = {p = prime(n); k = 0; while ((p+k) % 10 != 5, k++); k;} \\ Michel Marcus, Aug 25 2013

A130973 Number of primes between successive pairs of twin primes, for a(n) > 0.

Original entry on oeis.org

1, 1, 2, 1, 4, 3, 4, 2, 1, 3, 1, 2, 3, 10, 4, 7, 4, 3, 2, 1, 2, 18, 2, 2, 17, 1, 2, 6, 9, 3, 1, 1, 1, 8, 3, 2, 15, 1, 4, 1, 1, 7, 7, 4, 4, 3, 4, 1, 1, 7, 2, 5, 1, 5, 18, 2, 5, 4, 3, 1, 5, 1, 18, 12, 2, 8, 1, 4, 2, 5, 4, 1, 1, 1, 9, 10

Offset: 1

Omar E. Pol, Aug 23 2007

a(k) corresponds to the k-th term in the isolated prime sequence A007510 or A134797. a(1) corresponds to 23. a(2) corresponds to 37. a(3) corresponds to 47 and 53. - Enrique Navarrete, Jan 28 2017

Lengths of the runs of consecutive integers in A176656. - R. J. Mathar, Feb 19 2017

C. K. Caldwell, The Prime Pages.
Omar E. Pol, Determinacion geometrica de los numeros primos y perfectos.

Cf. A001223, A007510 (isolated primes), A027883, A048614, A048198, A052011, A052012, A061273, A076777, A073784, A082602, A088700, A179067 (clusters of twin primes).

cp's OEIS Frontend

A321972 Numbers k for which A048198(k)=3.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Maple

Mathematica

A048199 Distance of primes to next odd multiple of 5 (where n mod 10 = 5).

Views

Author

Keywords

Examples

Crossrefs

Programs

PARI

A130973 Number of primes between successive pairs of twin primes, for a(n) > 0.

Views

Author

Keywords

Comments

Links

Crossrefs