login
A309877
a(n) is the smallest number k such that the difference between the next prime greater than k and k equals n.
1
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
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
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Aug 21 2019
STATUS
approved