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A132861
Smallest number at distance 3n from nearest prime (variant 2).
1
2, 26, 53, 532, 211, 1342, 2179, 15704, 16033, 31424, 24281, 31430, 31433, 155960, 58831, 360698, 206699, 370312, 370315, 492170, 1357261, 1357264, 1357267, 2010802, 2010805, 4652428, 12485141, 17051788, 17051791, 17051794, 11117213, 20831416, 10938023, 20831422
OFFSET
0,1
COMMENTS
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.
LINKS
Michael S. Branicky, Table of n, a(n) for n = 0..76
Michael S. Branicky, Python program
FORMULA
a(n) = min {m : A051700(m) = 3n} for n > 0.
a(n) = A051652(3*n). [From R. J. Mathar, Jul 22 2009]
MAPLE
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);
PROG
(Python) # see link for faster program
from sympy import prevprime, nextprime
def A051700(n):
return [2, 1, 1][n] if n < 3 else min(n-prevprime(n), nextprime(n)-n)
def a(n):
if n == 0: return 2
m = 0
while A051700(m) != 3*n: m += 1
return m
print([a(n) for n in range(13)]) # Michael S. Branicky, Feb 26 2021
CROSSREFS
Sequence in context: A084298 A001772 A199206 * A210848 A247957 A152997
KEYWORD
nonn
AUTHOR
R. J. Mathar, Nov 18 2007
EXTENSIONS
7 more terms from R. J. Mathar, Jul 22 2009
4 more terms from R. J. Mathar, Aug 21 2018
a(30) and beyond and edits from Michael S. Branicky, Feb 26 2021
STATUS
approved