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.

52, 2660, 14440, 14770, 53679, 59085, 93770, 101435, 488897, 1326547, 1708955, 3006960, 7917044, 8445638, 9134659, 9905820, 10064091, 11707299, 15212090, 34154721, 39238738, 48407196, 86730401, 161428391, 203306292, 243361040, 323734799, 510916782, 742150423

Offset

1,1

Links

Table of n, a(n) for n=1..29.

Example

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

Prog

(PARI)
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
(Haskell)
a247628 n = a247628_list !! (n-1)
a247628_list = filter f a216155_list where
   f x = any ((== 1) . a010057) [a002522 x .. a002378 x - 1]
-- Reinhard Zumkeller, Sep 26 2014
(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

Crossrefs

Cf. A000290, A000578.

Cf. A002378, A002522, A010057, subsequence of A216155.

Sequence in context: A134552 A004296 A097837 * A370188 A262272 A189908

Adjacent sequences: A247625 A247626 A247627 * A247629 A247630 A247631

Keyword

nonn

Author

Alex Ratushnyak, Sep 21 2014

Extensions

a(12)-a(23) from Michel Marcus, Sep 27 2014

a(24)-a(29) from Jon E. Schoenfield, Oct 11 2014

Status

approved