1,3

Charlton Harrison found a new record binary-decimal palindrome 11000101111000010101010110100001110100000100000101110000101101010101000011110100011_2 = 7475703079870789703075747_10 on Dec 01 2001. The binary string contains 83 digits! Since then he has added twenty more terms. - Robert G. Wilson v Jul 03 2006

M. R. Calandra, Integers which are palindromic in both decimal and binary notation, J. Rec. Math., 18 (No. 1, 1985-1986), 47.

S. Pilpel, Some More Double Palindromic Integers, J. Rec. Math., 18 (1985), 174-176.

Robert G. Wilson v, Table of n, a(n) for n = 1..101

P. De Geest, Palindromic numbers beyond base 10

Charlton Harrison, Binary/Decimal Palindromes

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]] ]] ]] ]]; palQ[n_Integer, base_Integer]:= Block[{idn = IntegerDigits[n, base]}, idn == Reverse[idn]]; l = {0}; a = 0; Do[a = NextPalindrome[a]; If[ palQ[a, 2], AppendTo[l, a]], {n, 1000000}]; l (from Robert G. Wilson v Sep 30 2004)

For number of terms less than or equal to 10^n, see A120764.

Cf. A007633, A029961, A029962, A029963, A029964, A029804, A029965, A029966, A029967, A029968, A029969, A029970, A029731, A097855, A099165.

Adjacent sequences: A007629 A007630 A007631 this_sequence A007633 A007634 A007635

Sequence in context: A131668 A119252 A081434 this_sequence A117996 A092046 A085951

base,nonn,nice

njas, Mira Bernstein, Robert G. Wilson v (rgwv(AT)rgwv.com)

One more term from George Russell (ger(AT)tzi.de), Nov 20 2000. Two further terms from Harvey P. Dale (hpd1(AT)nyu.edu), Mar 09 2001.

Further terms from George Russell (ger(AT)tzi.de), Nov 02 2001