login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A255830 Numbers D such that D^2 = A^4 + B^5 + C^6 for some positive integers A, B, C. 7
7, 9, 17, 33, 72, 89, 96, 99, 105, 137, 171, 213, 218, 240, 320, 459, 503, 513, 525, 616, 761, 792, 833, 1048, 1127, 1257, 1369, 1395, 1536, 1551, 2025, 2457, 2600, 2610, 3267, 3312, 3600, 3681, 4032, 4100, 4125, 4128, 4201, 4901, 4976, 5001, 5225, 5880, 5975, 6167 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The sequence has the infinite subsequence (4^n*(2^n+16), n=0,1,2,...), with corresponding (A,B,C) = (2^(n+2),2^(n+1),2^n).

See A256652 for terms whose square has more than one representation of the given form. See A256613 for the subsequence of terms such that A^2 + B^3 + C^4 is a square, cf. A180241. See A256091 for the analog for sums of 3rd, 4th and 5th power.

LINKS

Table of n, a(n) for n=1..50.

EXAMPLE

(A, B, C) = (1, 4, 2) = 1^4 + 4^5 + 2^6 = 1 + 1024 + 64 = 1089 = 33^2, so 33 is a term.

(A, B, C) = (1, 4, 8) = 1^4 + 4^5 + 8^6 = 1 + 1024 + 262144 = 263169 = 513^2, so 513 is a term.

PROG

(PARI) is_A255830(D)=my(B, C=0, D2C6); while(1<D2C6=D^2-C++^6, B=0; while(0<D2C6-B++^5, ispower(D^2-C^6-B^5, 4)&&return(1)))

for(D=1, 9999, is_A255830(D)&&print1(D", ")) \\ Converted to integer arithmetic by M. F. Hasler, May 01 2015

CROSSREFS

Cf. A256091, A256613, A180241, A180242, A256652.

Sequence in context: A022321 A194830 A183344 * A256613 A116484 A138749

Adjacent sequences:  A255827 A255828 A255829 * A255831 A255832 A255833

KEYWORD

nonn

AUTHOR

M. F. Hasler, Apr 06 2015

EXTENSIONS

Inserted a(4)=33, a(18)=513 and removed doublet 1257 by Lars Blomberg, Apr 26 2015

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 23 03:40 EDT 2020. Contains 337291 sequences. (Running on oeis4.)