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%I #12 Aug 23 2019 14:38:12
%S 1,0,8,7,24,23,90,89,118,117,116,115,114,113,526,525,524,523,888,887,
%T 1130,1129,1338,1337,1336,1335,1334,1333,1332,1331,1330,1329,1328,
%U 1327,9552,9551,15690,15689,15688,15687,15686,15685,15684,15683,19616,19615,19614,19613,19612,19611
%N a(n) is the smallest number k such that the difference between the next prime greater than k and k equals n.
%H Robert Israel, <a href="/A309877/b309877.txt">Table of n, a(n) for n = 1..282</a>
%F a(n) = min {k : A013632(k) = n}.
%e +------+------+-----+
%e | a(n) | next | gap |
%e | | prime| |
%e +------+------+-----+
%e | 1 | 2 | 1 |
%e | 0 | 2 | 2 |
%e | 8 | 11 | 3 |
%e | 7 | 11 | 4 |
%e | 24 | 29 | 5 |
%e | 23 | 29 | 6 |
%e | 90 | 97 | 7 |
%e | 89 | 97 | 8 |
%e +------+------+-----+
%p N:= 100:
%p A:= Vector(N,-1):
%p count:= 0: lastp:= 0:
%p while count < N do
%p p:= nextprime(lastp);
%p newvals:= select(t -> A[t]=-1, [$1..min(p-lastp,N)]);
%p count:= count+nops(newvals);
%p for k in newvals do A[k]:= p-k od;
%p lastp:= p;
%p od:
%p convert(A,list); # _Robert Israel_, Aug 23 2019
%t Table[SelectFirst[Range[0, 20000], NextPrime[#] - # == n &], {n, 1, 50}]
%o (PARI) a(n) = my(k=0); while(nextprime(k+1) - k != n, k++); k; \\ _Michel Marcus_, Aug 21 2019
%Y Cf. A000101, A000230, A007918, A007920, A013632, A051652, A075403, A077019, A151800.
%K nonn
%O 1,3
%A _Ilya Gutkovskiy_, Aug 21 2019
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