A230358 a(n) is the smallest number k > 0 such that k, k + 1, ... , k + n - 1 are nonprime numbers, but k + n is prime.
2, 1, 9, 8, 25, 24, 91, 90, 119, 118, 117, 116, 115, 114, 527, 526, 525, 524, 889, 888, 1131, 1130, 1339, 1338, 1337, 1336, 1335, 1334, 1333, 1332, 1331, 1330, 1329, 1328, 9553, 9552, 15691, 15690, 15689, 15688, 15687, 15686, 15685, 15684, 19617, 19616, 19615
Offset: 0
Keywords
Examples
a(0) = 2 because 2 is prime. a(1) = 1 because 1 is nonprime, but 1 + 1 = 2 is prime. a(2) = 9 because 9 and 10 are nonprimes, but 11 is prime. a(3) = 8 because 8, 9 and 10 are nonprimes, but 11 is prime.
Links
- Harvey P. Dale, Table of n, a(n) for n = 0..100
Crossrefs
Cf. A233418.
Programs
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Maple
for n from 0 to 50 do: ii:=0:for k from 1 to 10000 while(ii=0) do:i:=0:for m from 0 to n while(type(k+m,prime)=false ) do :i:=i+1:od:if i=n then ii:=1: printf(`%d, `,k):else fi:od:od: ~
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Mathematica
nn = 50; t = Table[0, {nn}]; cnt = 0; k = 0; While[cnt < nn, k++; i = 0; While[! PrimeQ[k + i], i++]; If[i < nn && t[[i + 1]] == 0, t[[i + 1]] = k; cnt++]]; t (* *** program from T. D. Noe adapted for this sequence - see A233418 *** *) Flatten[Table[SequencePosition[Table[If[PrimeQ[n],0,1],{n,30000}],PadLeft[ {0},k,1],1],{k,50}],1][[All,1]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, May 20 2018 *)