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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified April 15 20:34 EDT 2021. Contains 342977 sequences. (Running on oeis4.)