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

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A029952 Palindromic in base 5. 28
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

T. D. Noe, Table of n, a(n) for n = 1..10000

Javier Cilleruelo, Florian Luca and Lewis Baxter, Every positive integer is a sum of three palindromes, Mathematics of Computation, Vol. 87, No. 314 (2018), pp. 3023-3055, arXiv preprint, arXiv:1602.06208 [math.NT], 2017.

Patrick De Geest, Palindromic numbers beyond base 10.

Phakhinkon Phunphayap and Prapanpong Pongsriiam, Estimates for the Reciprocal Sum of b-adic Palindromes, 2019.

Index entries for sequences that are an additive basis, order 3.

FORMULA

Sum_{n>=2} 1/a(n) = 2.9200482... (Phunphayap and Pongsriiam, 2019). - Amiram Eldar, Oct 17 2020

MAPLE

# test for palindrome in base b, from N. J. A. Sloane, Sep 13 2015

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

(PARI) ispal(n, b=5)=my(d=digits(n, b)); d==Vecrev(d) \\ Charles R Greathouse IV, May 03 2020

CROSSREFS

Palindromes in bases 2 through 10: A006995, A014190, A014192, A029952, A029953, A029954, A029803, A029955, A002113.

Cf. A261917, A261918.

Sequence in context: A043708 A296697 A297256 * A140494 A048316 A037393

Adjacent sequences:  A029949 A029950 A029951 * A029953 A029954 A029955

KEYWORD

nonn,base,easy

AUTHOR

Patrick De Geest

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 December 1 05:33 EST 2021. Contains 349426 sequences. (Running on oeis4.)