A163497 -id:A163497 - cp's OEIS frontend

A154840 Distance to nearest cube different from n.

1, 1, 1, 2, 3, 3, 2, 1, 7, 1, 2, 3, 4, 5, 6, 7, 8, 9, 9, 8, 7, 6, 5, 4, 3, 2, 1, 19, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 37, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16

Offset: 0

R. J. Mathar, Nov 01 2009

Equals A074989(n) if this is not zero, else 1+A055400(n-1), the distance to the nearest cube < n.

			a(8)=7, because the two cubes below and above 8 are 1^3=1 and 3^3=27, and the distance to 1 is smaller, namely 8-1=7.

Cf. A066635, A163497.

distNearstDiffCub := proc(n) local iscbr ; iroot(n,3,'iscbr') ; if iscbr then 1+A055400(n-1); else A074989(n) ; end if; end proc;

dnc[n_]:=Module[{c=Surd[n,3]},If[IntegerQ[c],n-(c-1)^3,Min[n-Floor[ c]^3, Ceiling[c]^3-n]]]; Array[dnc,90,0] (* Harvey P. Dale, Mar 30 2019 *)

A164834 Numbers such that the two adjacent integers are a perfect cube and a prime.

Original entry on oeis.org

2, 28, 126, 728, 3374, 6858, 19682, 24390, 29790, 50652, 91126, 250048, 274626, 300762, 328510, 357912, 571788, 753570, 970298, 1157626, 1295028, 1442898, 1771560, 1860868, 2146688, 2146690, 2460374, 2924208, 3048624, 3442950, 3581578, 4492124, 5000212

Offset: 1

Gaurav Kumar, Aug 28 2009

nonn

Subsequence of A163497.

			2 is a term since 2 has adjacent numbers 1 (cube) and 3 (prime).
28 is a term since 28 has adjacent numbers 27 (cube) and 29 (prime).
728 is a term since 728 has adjacent numbers 727 (prime) and 729 (cube).

Alois P. Heinz, Table of n, a(n) for n = 1..10000 (first 1000 terms from Donovan Johnson)

Cf. A163497, A178228.

Select[Which[PrimeQ[ #+2],#+1,PrimeQ[ #-2],#-1,True,0]&/@(Range[1000]^3),#!=0&] (* Harvey P. Dale, Sep 29 2009 *)

from sympy import isprime
def aupto(limit):
  i, c, alst = 1, 1, []
  while c <= limit + 1:
    if isprime(c-2) and c-1 <= limit: alst.append(c-1)
    if isprime(c+2) and c+1 <= limit: alst.append(c+1)
    i += 1
    c = i**3
  return alst
print(aupto(5000212)) # Michael S. Branicky, Feb 28 2021

Edited by Zak Seidov, Aug 30 2009

a(20)-a(30) from Donovan Johnson, Sep 16 2009

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A154840 Distance to nearest cube different from n.

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