A127698 - OEIS

%I #16 Apr 03 2023 10:36:11

%S 0,2,6,12,11,66,33,110,99,99,110,132,165,110,606,141,767,504,342,281,

%T 222,363,605,948,303,848,504,1251,1010,969,1029,1190,1353,726,1190,

%U 666,1332,1010,888,867,848,1029,1212,1595,1089,6336,2882,9339,7887,6446

%N Sum of n-th triangular number and its reversal.

%C Gupta states in Prime Curios: "The smallest odd prime which can be represented as sum of a triangular number and its reverse, i.e., 10 + 01 = 11."

%H Alois P. Heinz, <a href="/A127698/b127698.txt">Table of n, a(n) for n = 0..14141</a>

%H G. L. Honaker, Jr. and Chris Caldwell, eds., <a href="https://t5k.org/curios/page.php?short=11">11</a>.

%F a(n) = A000217(n) + A004086(A000217(n)).

%e a(0) = 0 + 0 = 0.

%e a(1) = 1 + 1 = 2 is the even prime.

%e a(4) = 10 + 1 = 11 is an odd prime.

%e a(5) = 15 + 51 = 66 = A000217(10).

%e a(19) = 190 + 91 = 281 is an odd prime.

%e a(24) = 300 + 3 = 303.

%e a(35) = 630 + 36 = 666 = A000217(36).

%p a:= n-> (p-> parse(cat(p, "+", seq(p[-i],

%p        i=1..length(p)))))(""||(n*(n+1)/2)):

%p seq(a(n), n=0..60);  # _Alois P. Heinz_, Jun 19 2016

%t rev[n_] := FromDigits@ Reverse@ IntegerDigits@ n; t[n_] := n (n + 1)/2; Table[t@ n + rev@ t@ n, {n, 0, 49}] (* _Giovanni Resta_, Jun 19 2016 *)

%t #+IntegerReverse[#]&/@Accumulate[Range[0,50]] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Sep 20 2016 *)

%Y Cf. A000217, A004086.

%K base,easy,look,nonn

%O 0,2

%A _Jonathan Vos Post_, Apr 03 2007

%E Edited by _Giovanni Resta_, Jun 19 2016