A123291 -id:A123291 - cp's OEIS frontend

A022549 Sum of a square and a nonnegative cube.

0, 1, 2, 4, 5, 8, 9, 10, 12, 16, 17, 24, 25, 26, 27, 28, 31, 33, 36, 37, 43, 44, 49, 50, 52, 57, 63, 64, 65, 68, 72, 73, 76, 80, 81, 82, 89, 91, 100, 101, 108, 113, 121, 122, 125, 126, 127, 128, 129, 134, 141, 144, 145

Offset: 1

N. J. A. Sloane

It appears that there are no modular constraints on this sequence; i.e., every residue class of every integer has representatives here. - Franklin T. Adams-Watters, Dec 03 2009

A045634(a(n)) > 0. - Reinhard Zumkeller, Jul 17 2010

R. Zumkeller, Table of n, a(n) for n = 1..10000 - _Reinhard Zumkeller_, Jul 17 2010

Complement of A022550; A002760 and A179509 are subsequences.

Cf. A055394, A045634, A055393, A123291, A169618, A123364, A111925.

q=30; imax=q^2; Select[Union[Flatten[Table[x^2+y^3, {y,0,q^(2/3)}, {x,0,q}]]], #<=imax&] (* Vladimir Joseph Stephan Orlovsky, Apr 20 2011 *)

is(n)=for(k=0,sqrtnint(n,3), if(issquare(n-k^3), return(1))); 0 \\ Charles R Greathouse IV, Aug 24 2020

list(lim)=my(v=List(),t); for(k=0,sqrtnint(lim\=1,3), t=k^3; for(n=0,sqrtint(lim-t), listput(v,t+n^2))); Set(v) \\ Charles R Greathouse IV, Aug 24 2020

A123364 Primes of the form a^2 + b^3 (with repetition).

Original entry on oeis.org

2, 5, 17, 17, 31, 37, 43, 73, 89, 89, 101, 113, 127, 197, 223, 233, 233, 241, 257, 269, 283, 337, 347, 353, 359, 379, 401, 443, 449, 449, 487, 521, 577, 577, 593, 593, 599, 677, 701, 733, 743, 811, 827, 829, 919, 953, 1009, 1019, 1049, 1051, 1097, 1129, 1153

Offset: 1

Zak Seidov, Oct 12 2006

nonn

Primes in A022549, A123291. Cf. A066649 Primes of the form a^2 + b^3 (without repetition), with a, b > 0.

			Each of 17, 89, 233 appears two times because 17=3^2+2^3=4^2+1^3, 89=5^2+4^3=9^2+2^3, 233=13^2+4^3=15^2+2^3;
2089 appears three times because 2089=19^2+12^3=33^2+10^3=45^2+4^3;
65537 appears four times because 65537=122^2+37^3=219^2+26^3=255^2+8^3=256^2+1^3.

Vincenzo Librandi, Table of n, a(n) for n = 1..200

Cf. A022549, A066649, A123291.

t={}; Do[AppendTo[t, n^2+m^3], {n, 100},{m, 100}]; Take[Select[Sort[t], PrimeQ], 60] (* Vladimir Joseph Stephan Orlovsky, Feb 10 2012 *)

cp's OEIS Frontend

A022549 Sum of a square and a nonnegative cube.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

PARI