A173638 The n-th semiprime plus n gives a palindrome in base 10.

1, 2, 11, 17, 20, 23, 25, 35, 40, 48, 53, 59, 69, 86, 94, 100, 128, 133, 138, 141, 145, 194, 211, 216, 224, 232, 282, 326, 450, 615, 665, 824, 876, 929, 1171, 1197, 1267, 1290, 1293, 1450, 1498, 1520, 1566, 1655, 1790, 1898, 2248, 2313, 2624, 2786, 2826, 2849, 2912, 3058, 3082, 3098, 3270, 3290, 3408, 3586, 3610, 3672, 3792, 3912, 3945, 3982, 4000

Offset: 1

Author

Jonathan Vos Post, Nov 23 2010

Keywords

• nonn
• base

Comments

This is to semiprimes A001358 as A115884 is to primes A000040.

Examples

			a(1) = 1 because 1st semiprime = 4, 4+1=5 is trivially a palindrome.
a(2) = 2 because 2nd semiprime = 6, 6+2=8 is trivially a palindrome.
a(3) = 11 because 11th semiprime = 33, 33+11=44 is nontrivially a palindrome.
a(4) = 17 because 17th semiprime = 49, 49+17=66 is nontrivially a palindrome.
a(5) = 20 because 20th semiprime = 57, 57+20=77 is nontrivially a palindrome.
a(8) = 35 because 35th semiprime = 106, 106+35=141 is nontrivially a palindrome.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

A001358, A002113, A115884, A100493.

Programs

Mathematica

Module[{nn=20000,sems},sems=Select[Range[nn],PrimeOmega[#]==2&]; Select[ Thread[{Range[Length[sems]],sems}],Total[ #]==IntegerReverse[Total[ #]]&]] [[All,1]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Oct 08 2016 *)

Formula

{n: n + A001358(n) is in A002113} == {n: n + A001358(n) = R(n)} == {n: n + A001358(n) = A004086(n)}.