A104182 - OEIS

%I #13 Feb 16 2025 08:32:56

%S 1,2,3,4,6,5,7,8,9,252,11,55,66,1001,2002,3003,5005,8008,171,969,22,

%T 646646,1771,33,595,666,3262623,44,77,88,99,101,5995,111,121,131,8778,

%U 141,151,161,15051,181,191,202,212,222,232,242,262,272,282,292

%N Palindromes in the order in which they appear in Pascal's triangle, without repetition.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PascalsTriangle.html">Pascal's Triangle</a>

%e Some rows of Pascal's Triangle:

%e Row 9 = {1, 9, 36, 84, 126, 126, 84, 36, 9, 1}

%e Row 10 = {1, 10, 45, 120, 210, 252, 210, 120, 45, 10, 1}

%e Row 1l = {1, 11, 55, 165, 330, 462, 462, 330, 165, 55, 11, 1}

%e Looking at this we see the palindromes of 9, 252, 11 and 55 in their order of appearance, without repetition.

%t DeleteDuplicates[Select[Flatten[Table[Binomial[n,m],{n,0,300},{m,0,n}]], IntegerDigits[#]==Reverse[IntegerDigits[#]]&]] (* _Harvey P. Dale_, May 04 2014 *)

%o (PARI) ispal(v) = {for(i=1, #v\2, if (v[i] != v[#v-i+1], return(0));); return(1);}; lista(n) = {ret = vector(0); for (i=1, n, for (j=1, i, numb = binomial(i, j); if (ispal(digits(numb)), if (! vecsearch(vecsort(ret), numb), ret = concat(ret, numb));););); print(ret);} \\ _Michel Marcus_, Jun 08 2013

%Y Cf. A051641.

%K nonn,base,changed

%O 1,2

%A Andrew G. West (WestA(AT)wlu.edu), Mar 29 2005

%E More terms from _Michel Marcus_, Jun 08 2013