Search: a261917 -id:a261917
|
| |
|
|
A029952
|
|
Palindromic in base 5.
|
|
+10
30
|
|
|
|
0, 1, 2, 3, 4, 6, 12, 18, 24, 26, 31, 36, 41, 46, 52, 57, 62, 67, 72, 78, 83, 88, 93, 98, 104, 109, 114, 119, 124, 126, 156, 186, 216, 246, 252, 282, 312, 342, 372, 378, 408, 438, 468, 498, 504, 534, 564, 594, 624, 626, 651, 676, 701, 726, 756, 781, 806, 831
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,3
|
|
|
COMMENTS
|
Cilleruelo, Luca, & Baxter prove that this sequence is an additive basis of order (exactly) 3. - Charles R Greathouse IV, May 03 2020
|
|
|
LINKS
|
|
|
|
FORMULA
|
Sum_{n>=2} 1/a(n) = 2.9200482... (Phunphayap and Pongsriiam, 2019). - Amiram Eldar, Oct 17 2020
|
|
|
MAPLE
|
b:=5;
ispal := proc(n) global b; local t1, t2, i;
if n <= b-1 then return(1); fi;
t1:=convert(n, base, b); t2:=nops(t1);
for i from 1 to floor(t2/2) do
if t1[i] <> t1[t2+1-1] then return(-1); fi;
od: return(1); end;
lis:=[]; for n from 0 to 100 do if ispal(n) = 1 then lis:=[op(lis), n]; fi; od: lis;
|
|
|
MATHEMATICA
|
f[n_, b_] := Module[{i=IntegerDigits[n, b]}, i==Reverse[i]]; lst={}; Do[If[f[n, 5], AppendTo[lst, n]], {n, 1000}]; lst (* Vladimir Joseph Stephan Orlovsky, Jul 08 2009 *)
Select[Range[0, 1000], IntegerDigits[#, 5]==Reverse[IntegerDigits[#, 5]]&] (* Harvey P. Dale, Oct 24 2020 *)
|
|
|
PROG
|
(Magma) [n: n in [0..900] | Intseq(n, 5) eq Reverse(Intseq(n, 5))]; // Vincenzo Librandi, Sep 09 2015
(Python)
from gmpy2 import digits
if n == 1: return 0
y = 5*(x:=5**(len(digits(n>>1, 5))-1))
return int((c:=n-x)*x+int(digits(c, 5)[-2::-1]or'0', 5) if n<x+y else (c:=n-y)*y+int(digits(c, 5)[-1::-1]or'0', 5)) # Chai Wah Wu, Jun 13 2024
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
nonn,base,easy
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
| |
|
|
A261918
|
|
Numbers which in base 5 are neither palindromes nor the sum of two palindromes.
|
|
+10
3
|
|
|
|
11, 17, 23, 51, 131, 141, 146, 147, 149, 151, 153, 154, 163, 164, 169, 173, 175, 177, 179, 181, 184, 185, 194, 195, 199, 200, 201, 203, 205, 206, 211, 215, 221, 225, 226, 229, 231, 236, 237, 241, 251, 259, 261, 262, 263, 266, 267, 271, 281, 287, 289, 291, 296, 297
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,1
|
|
|
COMMENTS
|
The terms less than 20000, and conjecturally all terms, are the sum of three base 5 palindromes.
|
|
|
LINKS
|
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
nonn,base
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
Search completed in 0.004 seconds
|
