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
Keywords
Examples
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
Programs
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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
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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
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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
Extensions
a(12)-a(23) from Michel Marcus, Sep 27 2014
a(24)-a(29) from Jon E. Schoenfield, Oct 11 2014