A127698 Sum of n-th triangular number and its reversal.

0, 2, 6, 12, 11, 66, 33, 110, 99, 99, 110, 132, 165, 110, 606, 141, 767, 504, 342, 281, 222, 363, 605, 948, 303, 848, 504, 1251, 1010, 969, 1029, 1190, 1353, 726, 1190, 666, 1332, 1010, 888, 867, 848, 1029, 1212, 1595, 1089, 6336, 2882, 9339, 7887, 6446

Offset

0,2

Comments

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."

Links

Alois P. Heinz, Table of n, a(n) for n = 0..14141

G. L. Honaker, Jr. and Chris Caldwell, eds., 11.

Formula

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

Example

a(0) = 0 + 0 = 0.
a(1) = 1 + 1 = 2 is the even prime.
a(4) = 10 + 1 = 11 is an odd prime.
a(5) = 15 + 51 = 66 = A000217(10).
a(19) = 190 + 91 = 281 is an odd prime.
a(24) = 300 + 3 = 303.
a(35) = 630 + 36 = 666 = A000217(36).

Maple

a:= n-> (p-> parse(cat(p, "+", seq(p[-i],
       i=1..length(p)))))(""||(n*(n+1)/2)):
seq(a(n), n=0..60);  # Alois P. Heinz, Jun 19 2016

Mathematica

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

Crossrefs

Cf. A000217, A004086.

Sequence in context: A009230 A354421 A069491 * A379620 A379518 A130503

Adjacent sequences: A127695 A127696 A127697 * A127699 A127700 A127701

Keyword

base,easy,look,nonn

Author

Jonathan Vos Post, Apr 03 2007

Extensions

Edited by Giovanni Resta, Jun 19 2016

Status

approved