A216237 Happy palindromic numbers.

1, 7, 44, 262, 313, 383, 404, 464, 565, 656, 818, 888, 989, 1221, 1771, 1881, 2112, 3553, 4004, 4554, 4774, 5335, 5445, 5555, 7117, 7447, 7887, 8118, 8778, 11311, 11811, 12021, 12321, 12921, 14641, 15451, 15951, 17071, 17371, 18081, 18381, 20602, 21012

Offset: 1

Author

Jayanta Basu, Mar 14 2013

Keywords

• nonn
• base
• easy

Comments

That is, happy numbers (A007770) that are palindromic (A002113).

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A002113, A007770.

Programs

Haskell

a216237 n = a216237_list !! (n-1)
a216237_list = filter ((== 1) . a136522) a007770_list
-- Reinhard Zumkeller, Mar 15 2013

Mathematica

palQ[n_] := Block[{d=IntegerDigits@n}, d == Reverse@d]; happyQ[n_] := Block[{w = n}, While[w > 6, w = Total[IntegerDigits[w]^2]]; w == 1]; Select[Range[21012], palQ[#] && happyQ[#] &] (* Giovanni Resta, Mar 14 2013 *)

Formula

A103369(a(n)) * A136522(a(n)) = 1. - Reinhard Zumkeller, Mar 15 2013