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

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

Cf. A132470, A051700.

Sequence in context: A084298 A001772 A199206 * A210848 A247957 A152997

Adjacent sequences: A132858 A132859 A132860 * A132862 A132863 A132864

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