OFFSET
1,2
COMMENTS
Multiplicative closure of A002385; A051038 and A046368 are subsequences. - Reinhard Zumkeller, Apr 11 2011
LINKS
FORMULA
Sum_{n>=1} 1/a(n) = Product_{p in A002385} p/(p-1) = 5.0949... - Amiram Eldar, Sep 27 2020
EXAMPLE
10 = 2 * 5 is a term since both 2 and 5 are palindromes.
110 = 2 * 5 * 11 is a term since 2, 5 and 11 are palindromes.
MAPLE
N:= 5: # to get all terms of up to N digits
digrev:= proc(t) local L; L:= convert(t, base, 10);
add(L[-i-1]*10^i, i=0..nops(L)-1);
end proc:
PPrimes:= [2, 3, 5, 7, 11]:
for d from 3 to N by 2 do
m:= (d-1)/2;
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)]);
od:
PPrimes:= map(op, [PPrimes]):
M:= 10^N:
B:= Vector(M);
B[1]:= 1:
for p in PPrimes do
for k from 1 to floor(log[p](M)) do
R:= [$1..floor(M/p^k)];
B[p^k*R] := B[p^k*R] + B[R]
od
od:
select(t -> B[t] > 0, [$1..M]); # Robert Israel, Jul 05 2015
# alternative
isA033620:= proc(n)
for d in numtheory[factorset](n) do
if not isA002113(op(1, d)) then
return false;
end if;
end do;
true ;
end proc:
for n from 1 to 300 do
if isA033620(n) then
printf("%d, ", n) ;
end if;
end do: # R. J. Mathar, Sep 09 2015
MATHEMATICA
palQ[n_]:=Reverse[x=IntegerDigits[n]]==x; Select[Range[131], And@@palQ/@First/@FactorInteger[#]&] (* Jayanta Basu, Jun 05 2013 *)
PROG
(Haskell)
a033620 n = a033620_list !! (n-1)
a033620_list = filter chi [1..] where
chi n = a136522 spf == 1 && (n' == 1 || chi n') where
n' = n `div` spf
spf = a020639 n -- cf. A020639
-- Reinhard Zumkeller, Apr 11 2011
(PARI) ispal(n)=n=digits(n); for(i=1, #n\2, if(n[i]!=n[#n+1-i], return(0))); 1
is(n)=if(n<13, n>0, vecmin(apply(ispal, factor(n)[, 1]))) \\ Charles R Greathouse IV, Feb 06 2013
(Python)
from sympy import isprime, primefactors
def pal(n): s = str(n); return s == s[::-1]
def ok(n): return all(pal(f) for f in primefactors(n))
print(list(filter(ok, range(1, 132)))) # Michael S. Branicky, Apr 06 2021
CROSSREFS
KEYWORD
nonn,base,easy
AUTHOR
N. J. A. Sloane, May 17 1998
STATUS
approved