A333016 Smallest palindromic number >= 2^n.

1, 2, 4, 8, 22, 33, 66, 131, 262, 515, 1111, 2112, 4114, 8228, 16461, 32823, 65556, 131131, 262262, 524425, 1049401, 2097902, 4194914, 8388838, 16777761, 33555533, 67111176, 134222431, 268444862, 536878635, 1073773701, 2147557412, 4294994924, 8589999858, 17179897171

Offset

0,2

Links

Chai Wah Wu, Table of n, a(n) for n = 0..3321

Formula

a(n) = A262038(A000079(n)). - Michel Marcus, May 04 2020

Example

a(10) = 1111, because 2^10 = 1024 and 1111 is the smallest palindromic number >= 1024.

Mathematica

spn[n_]:=Module[{k=2^n}, While[!PalindromeQ[k], k++]; k]; Array[spn, 40, 0] (* Harvey P. Dale, Jun 12 2023 *)
nP[cn_Integer]:=Module[{s, len, half, left, pal, fdpal}, s=IntegerDigits[cn]; len=Length[s]; half=Ceiling[len/2]; left=Take[s, half]; pal=Join[left, Reverse[Take[left, Floor[len/2]]]]; fdpal=FromDigits[pal]; Which[cn==9, 11, fdpal>cn, fdpal, True, left=IntegerDigits[FromDigits[left]+1]; pal=Join[left, Reverse[Take[left, Floor[len/2]]]]; FromDigits[pal]]]; Table[nP[2^n-1], {n, 0, 35}] (* Harvey P. Dale, Nov 16 2025 *)

Prog

(PARI) a(n) = for(k=2^n, oo, if(Vecrev(v=digits(k))==v, return(k))); \\ Jinyuan Wang, Mar 05 2020

Crossrefs

Cf. A000079, A002113, A262038, A333770.

Sequence in context: A262345 A192149 A115778 * A295628 A027713 A155765

Adjacent sequences: A333013 A333014 A333015 * A333017 A333018 A333019

Keyword

nonn,base

Author

Eder Vanzei, Mar 05 2020

Extensions

a(9) corrected by and more terms from Jinyuan Wang, Mar 05 2020

Status

approved