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
Keywords
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
Programs
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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
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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}.
Comments