A099280 2^n-th palindromic number.

1, 2, 4, 8, 77, 232, 555, 2992, 15751, 41314, 92529, 1049401, 3097903, 7193917, 63855836, 227696722, 555373555, 3107337013, 16214541261, 42428982424, 94857775849, 1097153517901, 3194305034913, 7388609068837, 67772177127776

Offset

0,2

Links

Chai Wah Wu, Table of n, a(n) for n = 0..1661

Mathematica

NextPalindrome[n_] := Block[ {l = Floor[ Log[10, n] + 1], idn = IntegerDigits[n]}, If[ Union[ idn] == {9}, Return[n + 2], If[l < 2, Return[n + 1], If[ FromDigits[ Reverse[ Take[ idn, Ceiling[l/2]]]] FromDigits[ Take[ idn, -Ceiling[l/2]]], FromDigits[ Join[ Take[ idn, Ceiling[l/2]], Reverse[ Take[ idn, Floor[l/2]]] ]], idfhn = FromDigits[ Take[ idn, Ceiling[l/2]]] + 1; idp = FromDigits[ Join[ IntegerDigits[ idfhn], Drop[ Reverse[ IntegerDigits[ idfhn]], Mod[l, 2]]]] ]]]]; k = 1; np = 0; Do[ While[np = NextPalindrome[np]; k != 2^n, k++ ]; Print[np], {n, 26}]

Prog

(Python)
def A099280(n):
    if n == 0: return 1
    m = 1<<n-1
    k = (m<<1)+1
    y = 10*(x:=10**(len(str(m))-1))
    return (c:=k-x)*x+int(str(c)[-2::-1]or 0) if k<x+y else (c:=k-y)*y+int(str(c)[-1::-1]or 0) # Chai Wah Wu, Jun 13 2024

Crossrefs

Cf. A083816.

Sequence in context: A204548 A018532 A270381 * A018560 A087375 A018580

Adjacent sequences: A099277 A099278 A099279 * A099281 A099282 A099283

Keyword

base,nonn

Author

Robert G. Wilson v, Oct 04 2004

Status

approved