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User: Maxim Veselov

Maxim Veselov has authored 2 sequences.

A309787 Palindromes whose product of digits are palindromes with at least two digits.

676, 777, 16761, 17771, 23732, 32723, 61716, 71717, 1167611, 1177711, 1237321, 1327231, 1617161, 1717171, 2137312, 2317132, 3127213, 3217123, 6117116, 7117117, 111676111, 111777111, 112373211, 113272311, 116171611, 117171711, 121373121, 123171321

Offset: 1

Maxim Veselov, Nov 11 2019

For n < 40 every term relates to 676 or 777.

			For 676: 6*7*6 = 252.
For 1717171: 1*7*1*7*1*7*1 = 343.

Chai Wah Wu, Table of n, a(n) for n = 1..10912

Cf. A002113, A117055

f:=func; g:=func; [k:k in [1..10000000]| f(k) and f(&*Intseq(k)) and g(k)]; // Marius A. Burtea, Nov 12 2019

ispali:= proc(n) option remember; local L,i;
L:= convert(n,base,10);
andmap(i -> L[i]=L[-i], [$1..floor(nops(L)/2)])
end proc:
P[1]:= [$1..9]:
P[2]:= [seq(11*i,i=1..9)]:
for d from 3 to 13 do
  P[d]:= [seq(seq((10^(d-1)+1)*i+10*x, x=P[d-2]),i=1..9)]
od:
filter:= proc(n) local p; p:= convert(convert(n,base,10),`*`);
  p >= 11 and ispali(p)
end proc:
map(op,[seq(select(filter, P[d]),d=1..13)]); # Robert Israel, Nov 14 2019

pd[n_] := Times @@ IntegerDigits[n]; aQ[n_] := PalindromeQ[n] && (p = pd[n]) > 9 && PalindromeQ[p]; Select[Range[10^7], aQ] (* Amiram Eldar, Nov 12 2019 *)

Corrected by Robert Israel, Nov 14 2019

A329100 Composite palindromes whose divisors > 1 are all nontrivial palindromes (i.e., palindromes with at least two digits).

Original entry on oeis.org

121, 1111, 1331, 1441, 1661, 1991, 3443, 3883, 7997, 10201, 12221, 13231, 14641, 15251, 15851, 18281, 19291, 31613, 35653, 37673, 37873, 38683, 112211, 113311, 115511, 116611, 124421, 125521, 134431, 136631, 139931, 145541, 146641, 157751, 167761, 169961, 176671

Offset: 1

Maxim Veselov, Nov 04 2019

This is the intersection of A062687 and A038511.
From Chai Wah Wu, Nov 08 2019 : (Start)
All terms start and end with the digits 1,3,7 or 9.
First term with 3 prime factors: 1331 = 11^3.
First term with 3 distinct prime factors: 145541 = 11*101*131.
First term with 4 prime factors: 14641 = 11^4.
First term with 5 prime factors: 1478741 = 11^4*101.
No term with more than 3 distinct prime factors or more than 5 prime factors among first 10000 terms.
(End)

			For k = 1331, its divisors > 1 are 11, 121 and 1331, all of which are palindromes with at least two digits, so 1331 is a term.
For k = 167761, its divisors > 1 are 11, 101, 151, 1111, 1661, 15251 and 167761, all of which are palindromes with at least two digits, so 167761 is a term.

Chai Wah Wu, Table of n, a(n) for n = 1..10000

Cf. A008364, A038511, A062687.

aQ[n_] := CompositeQ[n] && AllTrue[Rest @ Divisors[n], # > 10 && PalindromeQ @ IntegerDigits[#] &]; Select[Range[200000], aQ] (* Amiram Eldar, Nov 06 2019 *)

isA329100(n) = if((n>1) && !isprime(n) && gcd(n,210)==1, {d = divisors(n); rd = vector(#d, i, subst(Polrev(digits(d[i])), x, 10)); (d == rd); }, 0) \\ Jianing Song, Nov 06 2019, based on the program of A062687

More terms from Jianing Song, Nov 06 2019

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User: Maxim Veselov

A309787 Palindromes whose product of digits are palindromes with at least two digits.

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