This site is supported by donations to The OEIS Foundation.

Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 5000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A033620 Numbers all of whose prime factors are palindromes. 7

%I

%S 1,2,3,4,5,6,7,8,9,10,11,12,14,15,16,18,20,21,22,24,25,27,28,30,32,33,

%T 35,36,40,42,44,45,48,49,50,54,55,56,60,63,64,66,70,72,75,77,80,81,84,

%U 88,90,96,98,99,100,101,105,108,110,112,120,121,125,126,128,131

%N Numbers all of whose prime factors are palindromes.

%C Multiplicative closure of A002385; A051038 and A046368 are subsequences. [_Reinhard Zumkeller_, Apr 11 2011]

%H Ivan Neretin, <a href="/A033620/b033620.txt">Table of n, a(n) for n = 1..10550</a>

%p N:= 5: # to get all terms of up to N digits

%p digrev:= proc(t) local L; L:= convert(t,base,10);

%p add(L[-i-1]*10^i,i=0..nops(L)-1);

%p end proc:

%p PPrimes:= [2,3,5,7,11]:

%p for d from 3 to N by 2 do

%p m:= (d-1)/2;

%p PPrimes:= PPrimes, select(isprime,[seq(seq(n*10^(m+1)+y*10^m+digrev(n), y=0..9), n=10^(m-1)..10^m-1)]);

%p od:

%p PPrimes:= map(op,[PPrimes]):

%p M:= 10^N:

%p B:= Vector(M);

%p B[1]:= 1:

%p for p in PPrimes do

%p for k from 1 to floor(log[p](M)) do

%p R:= [\$1..floor(M/p^k)];

%p B[p^k*R] := B[p^k*R] + B[R]

%p od

%p od:

%p select(t -> B[t] > 0, [\$1..M]); # _Robert Israel_, Jul 05 2015

%p # alternative

%p isA033620:= proc(n)

%p for d in numtheory[factorset](n) do

%p if not isA002113(op(1,d)) then

%p return false;

%p end if;

%p end do;

%p true ;

%p end proc:

%p for n from 1 to 300 do

%p if isA033620(n) then

%p printf("%d,",n) ;

%p end if;

%p end do: # _R. J. Mathar_, Sep 09 2015

%t palQ[n_]:=Reverse[x=IntegerDigits[n]]==x; Select[Range[131],And@@palQ/@First/@FactorInteger[#]&] (* _Jayanta Basu_, Jun 05 2013 *)

%o (Haskell)

%o a033620 n = a033620_list !! (n-1)

%o a033620_list = filter chi [1..] where

%o chi n = a136522 spf == 1 && (n' == 1 || chi n') where

%o n' = n `div` spf

%o spf = a020639 n -- cf. A020639

%o -- _Reinhard Zumkeller_, Apr 11 2011

%o (PARI) ispal(n)=n=digits(n);for(i=1,#n\2,if(n[i]!=n[#n+1-i],return(0)));1

%o is(n)=if(n<13,n>0,vecmin(apply(ispal,factor(n)[,1]))) \\ _Charles R Greathouse IV_, Feb 06 2013

%K nonn,base,easy

%O 1,2

%A _N. J. A. Sloane_, May 17 1998

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 10 11:39 EST 2016. Contains 279001 sequences.