A164834 - OEIS

%I #25 Jul 16 2022 12:05:22

%S 2,28,126,728,3374,6858,19682,24390,29790,50652,91126,250048,274626,

%T 300762,328510,357912,571788,753570,970298,1157626,1295028,1442898,

%U 1771560,1860868,2146688,2146690,2460374,2924208,3048624,3442950,3581578,4492124,5000212

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

%C Subsequence of A163497.

%H Alois P. Heinz, <a href="/A164834/b164834.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 terms from Donovan Johnson)

%e 2 is a term since 2 has adjacent numbers 1 (cube) and 3 (prime).

%e 28 is a term since 28 has adjacent numbers 27 (cube) and 29 (prime).

%e 728 is a term since 728 has adjacent numbers 727 (prime) and 729 (cube).

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

%o (Python)

%o from sympy import isprime

%o def aupto(limit):

%o   i, c, alst = 1, 1, []

%o   while c <= limit + 1:

%o     if isprime(c-2) and c-1 <= limit: alst.append(c-1)

%o     if isprime(c+2) and c+1 <= limit: alst.append(c+1)

%o     i += 1

%o     c = i**3

%o   return alst

%o print(aupto(5000212)) # _Michael S. Branicky_, Feb 28 2021

%Y Cf. A163497, A178228.

%K nonn

%O 1,1

%A _Gaurav Kumar_, Aug 28 2009

%E Edited by _Zak Seidov_, Aug 30 2009

%E a(20)-a(30) from _Donovan Johnson_, Sep 16 2009