|
%I #6 May 01 2019 10:21:15
%S 2,0,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0
%N Number of palindromic decagonal (10-gonal) numbers of length n whose index is also palindromic.
%C Is there a nonzero term beyond a(12)?
%H P. De Geest, <a href="http://www.worldofnumbers.com/square.htm">Palindromic Squares</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PalindromicNumber.html">Palindromic Number</a>
%e There is only one palindromic decagonal number of length 3 whose index is also palindromic, 8->232. Thus, a(3)=1.
%t A307827 = {0, 1, 232, 27972, 76867, 25555552, 7154664517, 158229922851, 2028787878202, 2040061600402, 2733623263372, 52667666676625, 675972505279576, 28519896169891582, 73542836563824537, 74529570707592547, 25552469511596425552, 27835145788754153872, 62740719088091704726, 67047523077032574076, 77979812588521897977, 107838025535520838701};
%t A307829 = {0, 1, 8, 84, 139, 2528, 42293, 198891, 712178, 714154, 826684, 3628625, 12999736, 84439174, 135593913, 136500523, 2527472528, 2637951184, 3960451966, 4094127596, 4415308953, 5192254461};
%t Table[Length[ Select[A307829[[Table[ Select[Range[20], IntegerLength[A307827[[#]]] == n || (n == 1 && A307827[[#]] == 0) &], {n, 20}][[n]]]], PalindromeQ[#] &]], {n, 20}]
%Y Cf. A001107, A307827, A307829, A307830, A307831, A307808.
%K nonn,base,hard,more
%O 1,1
%A _Robert Price_, Apr 30 2019
|
