cp's OEIS Frontend

A247628 Numbers n such that there is a cube strictly between n^2 and n^2+n, and a square strictly between n^3 and n^3+n.

%I A247628 #21 Oct 12 2014 00:54:37
%S A247628 52,2660,14440,14770,53679,59085,93770,101435,488897,1326547,1708955,
%T A247628 3006960,7917044,8445638,9134659,9905820,10064091,11707299,15212090,
%U A247628 34154721,39238738,48407196,86730401,161428391,203306292,243361040,323734799,510916782,742150423
%N A247628 Numbers n such that there is a cube strictly between n^2 and n^2+n, and a square strictly between n^3 and n^3+n.
%e A247628 52 is in the sequence because 2704 (52^2) < 2744 (14^3) < 2756 (52^2+52) and also 140608 (52^3) < 140625 (375^2) < 140660 (52^3+52). - _Michel Marcus_, Sep 26 2014
%o A247628 (PARI)
%o A247628 for(n=1,10^5,c=0;for(i=n^2+1,n^2+n-1,if(ispower(i)&&ispower(i)%3==0,c++;break));for(j=n^3+1,n^3+n-1,if(issquare(j),c++;break));if(c==2,print1(n,", "))) \\ _Derek Orr_, Sep 26 2014
%o A247628 (Haskell)
%o A247628 a247628 n = a247628_list !! (n-1)
%o A247628 a247628_list = filter f a216155_list where
%o A247628    f x = any ((== 1) . a010057) [a002522 x .. a002378 x - 1]
%o A247628 -- _Reinhard Zumkeller_, Sep 26 2014
%o A247628 (PARI) lista(nn) = {for (n = 1, nn, c=0; cr=0; if (sqrtint(n^3) != sqrtint(n^3+n-1), while (c <= n^2, cr++;  c = cr^3); if (c < n^2 + n, print1(n, ", "));););} \\ after C program by _Alex Ratushnyak_, _Michel Marcus_, Sep 27 2014
%Y A247628 Cf. A000290, A000578.
%Y A247628 Cf. A002378, A002522, A010057, subsequence of A216155.
%K A247628 nonn
%O A247628 1,1
%A A247628 _Alex Ratushnyak_, Sep 21 2014
%E A247628 a(12)-a(23) from _Michel Marcus_, Sep 27 2014
%E A247628 a(24)-a(29) from _Jon E. Schoenfield_, Oct 11 2014