A309877 a(n) is the smallest number k such that the difference between the next prime greater than k and k equals n.

1, 0, 8, 7, 24, 23, 90, 89, 118, 117, 116, 115, 114, 113, 526, 525, 524, 523, 888, 887, 1130, 1129, 1338, 1337, 1336, 1335, 1334, 1333, 1332, 1331, 1330, 1329, 1328, 1327, 9552, 9551, 15690, 15689, 15688, 15687, 15686, 15685, 15684, 15683, 19616, 19615, 19614, 19613, 19612, 19611

Offset

1,3

Links

Robert Israel, Table of n, a(n) for n = 1..282

Formula

a(n) = min {k : A013632(k) = n}.

Example

+------+------+-----+
| a(n) | next | gap |
|      | prime|     |
+------+------+-----+
|   1  |   2  |  1  |
|   0  |   2  |  2  |
|   8  |  11  |  3  |
|   7  |  11  |  4  |
|  24  |  29  |  5  |
|  23  |  29  |  6  |
|  90  |  97  |  7  |
|  89  |  97  |  8  |
+------+------+-----+

Maple

N:= 100:
A:= Vector(N, -1):
count:= 0: lastp:= 0:
while count < N do
  p:= nextprime(lastp);
  newvals:= select(t -> A[t]=-1, [$1..min(p-lastp, N)]);
  count:= count+nops(newvals);
  for k in newvals do A[k]:= p-k od;
  lastp:= p;
od:
convert(A, list); # Robert Israel, Aug 23 2019

Mathematica

Table[SelectFirst[Range[0, 20000], NextPrime[#] - # == n &], {n, 1, 50}]

Prog

(PARI) a(n) = my(k=0); while(nextprime(k+1) - k != n, k++); k; \\ Michel Marcus, Aug 21 2019

Crossrefs

Cf. A000101, A000230, A007918, A007920, A013632, A051652, A075403, A077019, A151800.

Sequence in context: A302512 A126937 A282471 * A303311 A267093 A090099

Adjacent sequences: A309874 A309875 A309876 * A309878 A309879 A309880

Keyword

nonn

Author

Ilya Gutkovskiy, Aug 21 2019

Status

approved