A173638 - OEIS

%I #11 Oct 08 2016 11:34:47

%S 1,2,11,17,20,23,25,35,40,48,53,59,69,86,94,100,128,133,138,141,145,

%T 194,211,216,224,232,282,326,450,615,665,824,876,929,1171,1197,1267,

%U 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

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

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

%H Harvey P. Dale, <a href="/A173638/b173638.txt">Table of n, a(n) for n = 1..1000</a>

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

%e a(1) = 1 because 1st semiprime = 4, 4+1=5 is trivially a palindrome.

%e a(2) = 2 because 2nd semiprime = 6, 6+2=8 is trivially a palindrome.

%e a(3) = 11 because 11th semiprime = 33, 33+11=44 is nontrivially a palindrome.

%e a(4) = 17 because 17th semiprime = 49, 49+17=66 is nontrivially a palindrome.

%e a(5) = 20 because 20th semiprime = 57, 57+20=77 is nontrivially a palindrome.

%e a(8) = 35 because 35th semiprime = 106, 106+35=141 is nontrivially a palindrome.

%t 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 *)

%Y A001358, A002113, A115884, A100493.

%K nonn,base

%O 1,2

%A _Jonathan Vos Post_, Nov 23 2010