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

Author

Ilya Gutkovskiy, Aug 21 2019

Keywords

• nonn

Examples

			+------+------+-----+
| 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  |
+------+------+-----+
		

Links

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

Crossrefs

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

Programs

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}]
Module[{nn=20000,d},d=Table[{n,NextPrime[n]-n},{n,0,nn}];Table[SelectFirst[d,#[[2]]==k&],{k,50}]][[;;,1]] (* Harvey P. Dale, Mar 23 2025 *)

PARI

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

Formula

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