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

%I A164834 #25 Jul 16 2022 12:05:22
%S A164834 2,28,126,728,3374,6858,19682,24390,29790,50652,91126,250048,274626,
%T A164834 300762,328510,357912,571788,753570,970298,1157626,1295028,1442898,
%U A164834 1771560,1860868,2146688,2146690,2460374,2924208,3048624,3442950,3581578,4492124,5000212
%N A164834 Numbers such that the two adjacent integers are a perfect cube and a prime.
%C A164834 Subsequence of A163497.
%H A164834 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 A164834 2 is a term since 2 has adjacent numbers 1 (cube) and 3 (prime).
%e A164834 28 is a term since 28 has adjacent numbers 27 (cube) and 29 (prime).
%e A164834 728 is a term since 728 has adjacent numbers 727 (prime) and 729 (cube).
%t A164834 Select[Which[PrimeQ[ #+2],#+1,PrimeQ[ #-2],#-1,True,0]&/@(Range[1000]^3),#!=0&] (* _Harvey P. Dale_, Sep 29 2009 *)
%o A164834 (Python)
%o A164834 from sympy import isprime
%o A164834 def aupto(limit):
%o A164834   i, c, alst = 1, 1, []
%o A164834   while c <= limit + 1:
%o A164834     if isprime(c-2) and c-1 <= limit: alst.append(c-1)
%o A164834     if isprime(c+2) and c+1 <= limit: alst.append(c+1)
%o A164834     i += 1
%o A164834     c = i**3
%o A164834   return alst
%o A164834 print(aupto(5000212)) # _Michael S. Branicky_, Feb 28 2021
%Y A164834 Cf. A163497, A178228.
%K A164834 nonn
%O A164834 1,1
%A A164834 _Gaurav Kumar_, Aug 28 2009
%E A164834 Edited by _Zak Seidov_, Aug 30 2009
%E A164834 a(20)-a(30) from _Donovan Johnson_, Sep 16 2009