

A262038


Least palindrome >= n.


77



0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 11, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 77, 77, 77, 77, 77, 77, 77, 77, 77, 77
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OFFSET

0,3


COMMENTS

Could be called nextpalindrome() in analogy to the nextprime() function A007918. As for the latter (A151800), there is the variant "next strictly larger palindrome" which equals a(n+1), and thus differs from a(n) iff n is a palindrome; see PARI code.
Might also be called palindromic ceiling function in analogy to the name "palindromic floor" proposed for A261423.


LINKS

M. F. Hasler, Table of n, a(n) for n = 0..10000
Eric Weisstein's World of Mathematics, Palindromic Number
Wikipedia, Palindromic number
Index entries for sequences related to palindromes


MATHEMATICA

palQ[n_] := Block[{d = IntegerDigits@ n}, d == Reverse@ d]; Table[k = n; While[! palQ@ k, k++]; k, {n, 0, 80}] (* Michael De Vlieger, Sep 09 2015 *)


PROG

(PARI) {A262038(n, d=digits(n), p(d)=sum(i=1, #d\2, (10^(i1)+10^(#di))*d[i], if(bittest(#d, 0), 10^(#d\2)*d[#d\2+1])))= for(i=(#d+3)\2, #d, d[i]>d[#d+1i]&&break; (d[i]<d[#d+1i]i==#d)&&return(p(d))); n<10&&return(n); forstep(i=(#d+1)\2, 1, 1, d[i]++>9return(p(d)); d[i]=0); 10^#d+1} \\ For a function "next strictly larger palindrome", delete the i==#d and n<10... part.  M. F. Hasler, Sep 09 2015
(Haskell)
a262038 n = a262038_list !! n
a262038_list = f 0 a002113_list where
f n ps'@(p:ps) = p : f (n + 1) (if p > n then ps' else ps)
 Reinhard Zumkeller, Sep 16 2015


CROSSREFS

Cf. A002113, A261423, A262037.
Sequences related to palindromic floor and ceiling: A175298, A206913, A206914, A261423, A262038, and the large block of consecutive sequences beginning at A265509.
Sequence in context: A123241 A033862 A329201 * A265558 A082273 A256755
Adjacent sequences: A262035 A262036 A262037 * A262039 A262040 A262041


KEYWORD

nonn,base


AUTHOR

M. F. Hasler, Sep 08 2015


STATUS

approved



