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 A132470 Smallest number at distance exactly 3n from nearest prime. 3
 2, 26, 119, 532, 1339, 1342, 9569, 15704, 19633, 31424, 31427, 31430, 31433, 155960, 155963, 360698, 360701, 370312, 370315, 492170, 1357261, 1357264, 1357267, 2010802, 2010805, 4652428, 17051785, 17051788, 17051791, 17051794, 17051797, 20831416, 20831419, 20831422 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Let f(m)= A051699(m) = exact distance from m to its closest prime (including m itself). Then a(n) = min { m : f(m) = 3n}. - R. J. Mathar, Nov 18 2007 This sequence can be derived from the record prime gap sequences A002386 and A005250. In particular, for n > 0, a(n) = A002386(k) + 3*n where k is the least index such that A005250(k) >= 3*n. - Andrew Howroyd, Jan 04 2020 LINKS Andrew Howroyd, Table of n, a(n) for n = 0..258 FORMULA a(n) = min {m : A051699(m) = 3n}. - R. J. Mathar, Nov 18 2007 EXAMPLE a(3)=532 where 532+3*3 is prime and all numbers below 532 have a distance smaller or larger than 3n=9 to their nearest primes and there is no prime within a distance of 8 to 532. MAPLE A051699 := proc(m) if isprime(m) then 0 ; elif m <= 2 then op(m+1, [2, 1]) ; else min(nextprime(m)-m, m-prevprime(m)) ; fi ; end: A132470 := proc(n) local m ; if n = 0 then RETURN(2); else for m from 0 do if A051699(m) = 3 * n then RETURN(m) ; fi ; od: fi ; end: seq(A132470(n), n=0..18) ; # R. J. Mathar, Nov 18 2007 MATHEMATICA terms = 34; gaps = Cases[Import["https://oeis.org/A002386/b002386.txt", "Table"], {_, _}][[;; terms, 2]]; w[n_] := (NextPrime[gaps[[n]] + 1] - gaps[[n]])/6 // Floor; k = 1; a[0] = 2; For[n = 1, n <= terms, n++, While[w[k] < n, k++]; a[n] = gaps[[k]] + 3n]; a /@ Range[0, terms-1] (* Jean-François Alcover, Apr 09 2020, after Andrew Howroyd *) PROG (PARI) \\ here R(gaps) wants prefix of A002386 as vector. aA002386(lim)={my(L=List(), q=2, g=0); forprime(p=3, lim, if(p-q>g, listput(L, q); g=p-q); q=p); Vec(L)} R(gaps)={my(w=vector(#gaps, n, nextprime(gaps[n]+1) - gaps[n])\6, r=vector(w[#w]+1), k=1); r[1]=2; for(n=1, w[#w], while(w[k]= 3n, or (in A051728) that f(m) = 2n or only >= 2n? Probably there should be several sequences, to include all the possibilities in each case. - N. J. A. Sloane, Nov 18 2007. Added Nov 20 2007: R. J. Mathar has now clarified the definition of the present sequence. Corrected and extended by R. J. Mathar, Nov 18 2007 Terms a(19) and beyond from Andrew Howroyd, Jan 04 2020 STATUS approved

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Last modified September 26 05:07 EDT 2021. Contains 347664 sequences. (Running on oeis4.)