cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

A046349 Composite numbers with only palindromic prime factors.

Original entry on oeis.org

4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 27, 28, 30, 32, 33, 35, 36, 40, 42, 44, 45, 48, 49, 50, 54, 55, 56, 60, 63, 64, 66, 70, 72, 75, 77, 80, 81, 84, 88, 90, 96, 98, 99, 100, 105, 108, 110, 112, 120, 121, 125, 126, 128, 132, 135, 140, 144, 147, 150
Offset: 1

Views

Author

Patrick De Geest, Jun 15 1998

Keywords

Links

Crossrefs

Cf. A002385, A033620, A046350, A046351.

Programs

  • Maple
    isA046349 := proc(n)
    simplify(isA033620(n) and not isprime(n)) ;
end proc:
for n from 2 to 300 do
    if isA046349(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[4,150],!PrimeQ[#]&&And@@palQ/@First/@FactorInteger[#]&] (* Jayanta Basu, Jun 05 2013 *)
Select[Range[200],CompositeQ[#]&&AllTrue[FactorInteger[#][[All,1]],PalindromeQ]&] (* Harvey P. Dale, May 15 2022 *)
  • Python
    from sympy import isprime, primefactors
def pal(n): s = str(n); return s == s[::-1]
def ok(n): return not isprime(n) and all(pal(f) for f in primefactors(n))
print(list(filter(ok, range(4, 151)))) # Michael S. Branicky, Apr 06 2021

Formula

A033620 INTERSECT A002808. - R. J. Mathar, Sep 09 2015

A046350 Odd composite numbers with only palindromic prime factors.

Original entry on oeis.org

9, 15, 21, 25, 27, 33, 35, 45, 49, 55, 63, 75, 77, 81, 99, 105, 121, 125, 135, 147, 165, 175, 189, 225, 231, 243, 245, 275, 297, 303, 315, 343, 363, 375, 385, 393, 405, 441, 453, 495, 505, 525, 539, 543, 567, 573, 605, 625, 655, 675, 693, 707, 729, 735, 755
Offset: 1

Views

Author

Patrick De Geest, Jun 15 1998

Keywords

Links

Crossrefs

Cf. A002385, A033620, A046349, A046351.

Programs

  • Mathematica
    palQ[n_]:=Reverse[x=IntegerDigits[n]]==x; Select[Range[9,755,2],!PrimeQ[#]&&And@@palQ/@First/@FactorInteger[#]&] (* Jayanta Basu, Jun 05 2013 *)
Select[Range[9,800,2],CompositeQ[#]&&AllTrue[FactorInteger[#][[All,1]], PalindromeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Mar 08 2018 *)
  • Python
    from sympy import isprime, primefactors
def pal(n): s = str(n); return s == s[::-1]
def ok(n): return not isprime(n) and all(pal(f) for f in primefactors(n))
print(list(filter(ok, range(9, 756, 2)))) # Michael S. Branicky, Apr 06 2021

A161730 Palindromic numbers that are fixed points of the TITO operation (see A161594) and are not products of palindromic primes.

Original entry on oeis.org

72927, 76167, 434434, 868868, 1226221, 4778774, 5703075, 8755578, 9386839, 13488431, 43877834, 123848321, 564414465, 777555777, 1072772701, 1946776491, 9935115399, 12467976421, 52854045825, 74663436647, 83361616338, 95829592859
Offset: 1

Views

Author

Tanya Khovanova, Jun 17 2009

Keywords

Comments

The numbers in this sequence are palindromic numbers that are fixed points of the TITO operation and are not primes and are not in A046351.

Links

Crossrefs

Cf. A161594, A161597, A161598, A161600.

Programs

  • Mathematica
    reversepower[{n_, k_}] := FromDigits[Reverse[IntegerDigits[n]]]^k f[n_] := FromDigits[ Reverse[IntegerDigits[Times @@ Map[reversepower, FactorInteger[n]]]]] rev[n_] := FromDigits[Reverse[IntegerDigits[n]]] Select[Range[5000000], rev[ # ] == # && ! PrimeQ[ # ] && f[ # ] == # && Map[rev, Transpose[FactorInteger[ # ]][[1]]] != Transpose[FactorInteger[ # ]][[1]] &]
  • PARI
    for( d=1,19, my(p=10^((d+1)\2),q=10^(d%2)); for( i=p\10,p-1, my(n = i\q*p+R(i),f); A161594(n)==n || next; apply(R,f=factor(n)[,1])==f && next; print1(n",") )) /* uses definitions given in A161594 */ \\ M. F. Hasler, Jun 25 2009

Extensions

Edited by N. J. A. Sloane, Jun 23 2009
Terms beyond a(6) from M. F. Hasler, Jun 25 2009

A161732 Fixed points of the TITO operation (A161594) that are also composite palindromes.

Original entry on oeis.org

4, 6, 8, 9, 22, 33, 44, 55, 66, 77, 88, 99, 121, 202, 242, 252, 262, 303, 343, 363, 393, 404, 484, 505, 525, 606, 616, 626, 686, 707, 808, 909, 939, 1111, 1331, 1441, 1661, 1991, 2112, 2222, 2662, 2772, 2882, 3333, 3443, 3773, 3883, 3993, 4224, 4444, 5445
Offset: 1

Views

Author

Tanya Khovanova, Jun 17 2009

Keywords

Comments

This sequence is a proper superset of A046351 (palindromic composite numbers with only palindromic prime factors). The smallest number that doesn't belong to A046351 is 72927. The numbers that are in this sequence and are not in A046351 are given in A161730.

Links

Crossrefs

Cf. A161594, A161597, A161598, A161600, A046351

Programs

  • Mathematica
    reversepower[{n_, k_}] := FromDigits[Reverse[IntegerDigits[n]]]^k f[n_] := FromDigits[ Reverse[IntegerDigits[Times @@ Map[reversepower, FactorInteger[n]]]]] rev[n_] := FromDigits[Reverse[IntegerDigits[n]]] Select[Range[10000], f[ # ] == # && rev[ # ] == # && ! PrimeQ[ # ] &]

Extensions

Edited by N. J. A. Sloane, Jun 23 2009
Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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