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

1,2

Comments

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

Links

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

Formula

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

Example

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.

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 *)

Crossrefs

A001358, A002113, A115884, A100493.

Sequence in context: A038927 A105877 A309499 * A018420 A253474 A133410

Adjacent sequences: A173635 A173636 A173637 * A173639 A173640 A173641

Keyword

nonn,base

Author

Jonathan Vos Post, Nov 23 2010

Status

approved