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A132861 Smallest number at distance 3n from nearest prime (variant 2).

%I A132861 #17 Feb 28 2021 12:05:46
%S A132861 2,26,53,532,211,1342,2179,15704,16033,31424,24281,31430,31433,155960,
%T A132861 58831,360698,206699,370312,370315,492170,1357261,1357264,1357267,
%U A132861 2010802,2010805,4652428,12485141,17051788,17051791,17051794,11117213,20831416,10938023,20831422
%N A132861 Smallest number at distance 3n from nearest prime (variant 2).
%C A132861 Let f(m) be the distance to the nearest prime as defined in A051700(m). Then a(n) = min {m: f(m) = 3n} for n > 0. A132470 uses A051699(m) to define the distance. a(n) <= A132470(n) because here primes at the start or end of a prime gap of size 3n may be picked, which would be discarded in A132470 for n>0; this gives a chance to minimize m here further than in A132470.
%H A132861 Michael S. Branicky, <a href="/A132861/b132861.txt">Table of n, a(n) for n = 0..76</a>
%H A132861 Michael S. Branicky, <a href="/A132861/a132861.py.txt">Python program</a>
%F A132861 a(n) = min {m : A051700(m) = 3n} for n > 0.
%F A132861 a(n) = A051652(3*n). [From _R. J. Mathar_, Jul 22 2009]
%p A132861 A051700 := proc(m) if m <= 2 then op(m+1,[2,1,1]) ; else min(nextprime(m)-m,m-prevprime(m)) ; fi ; end: a := proc(n) local m ; if n = 0 then RETURN(2); else for m from 0 do if A051700(m) = 3 * n then RETURN(m) ; fi ; od: fi ; end: seq(a(n),n=0..18);
%o A132861 (Python) # see link for faster program
%o A132861 from sympy import prevprime, nextprime
%o A132861 def A051700(n):
%o A132861   return [2, 1, 1][n] if n < 3 else min(n-prevprime(n), nextprime(n)-n)
%o A132861 def a(n):
%o A132861   if n == 0: return 2
%o A132861   m = 0
%o A132861   while A051700(m) != 3*n: m += 1
%o A132861   return m
%o A132861 print([a(n) for n in range(13)]) # _Michael S. Branicky_, Feb 26 2021
%Y A132861 Cf. A132470, A051700.
%K A132861 nonn
%O A132861 0,1
%A A132861 _R. J. Mathar_, Nov 18 2007
%E A132861 7 more terms from _R. J. Mathar_, Jul 22 2009
%E A132861 4 more terms from _R. J. Mathar_, Aug 21 2018
%E A132861 a(30) and beyond and edits from _Michael S. Branicky_, Feb 26 2021