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

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

Author

Gaurav Kumar, Aug 28 2009

Keywords

• nonn

Comments

Subsequence of A163497.

Examples

			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).
		

Links

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

Crossrefs

Cf. A163497, A178228.

Programs

Mathematica

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

Python

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

Extensions

Edited by Zak Seidov, Aug 30 2009

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