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A262038 Least palindrome >= n. 75
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 (list; graph; refs; listen; history; text; internal format)
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^(i-1)+10^(#d-i))*d[i], if(bittest(#d, 0), 10^(#d\2)*d[#d\2+1])))= for(i=(#d+3)\2, #d, d[i]>d[#d+1-i]&&break; (d[i]<d[#d+1-i]||i==#d)&&return(p(d))); n<10&&return(n); forstep(i=(#d+1)\2, 1, -1, d[i]++>9||return(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: A262039 A123241 A033862 * A265558 A082273 A256755

Adjacent sequences:  A262035 A262036 A262037 * A262039 A262040 A262041

KEYWORD

nonn,base

AUTHOR

M. F. Hasler, Sep 08 2015

STATUS

approved

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Last modified May 22 15:13 EDT 2019. Contains 323480 sequences. (Running on oeis4.)