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.

A046356 Odd numbers with only palindromic prime factors whose sum is palindromic (counted with multiplicity).

Original entry on oeis.org

9, 15, 27, 45, 121, 495, 735, 875, 1331, 1701, 2025, 2101, 2121, 2525, 2751, 3171, 3275, 3775, 3801, 4525, 5445, 6573, 7413, 7825, 7833, 8043, 8085, 8595, 8767, 8825, 9325, 9575, 9625, 10201, 12005, 13231, 14641, 15251, 15267, 15897, 16527, 17161
Offset: 0

Views

Author

Patrick De Geest, Jun 15 1998

Keywords

Examples

			8767 = 11 * 797 -> 11 + 797 = 808 and 808 is a palindrome.

Crossrefs

Cf. A046355, A046357.

Programs

  • Mathematica
    palQ[n_] := Reverse[x=IntegerDigits[n]] == x; Select[Range[9,17170,2], !PrimeQ[#] && And@@palQ/@Join[{Total[Times@@@(x=FactorInteger[#])]}, First/@x]&] (* Jayanta Basu, Jun 05 2013 *)

A046357 Composite palindromes with only palindromic prime factors whose sum is palindromic (counted with multiplicity).

Original entry on oeis.org

4, 6, 8, 9, 121, 1331, 5445, 10201, 13231, 14641, 15251, 18281, 19291, 31613, 35653, 37673, 38683, 52525, 59895, 1030301, 1336331, 3192913, 8117118, 104060401, 134969431, 286121682, 319464913, 677707776
Offset: 1

Views

Author

Patrick De Geest, Jun 15 1998

Keywords

Examples

			319464913 = 10301 * 31013 and 10301 + 31013 = 41314 and all are palindromic.

Crossrefs

Cf. A046355, A046356.

Programs

  • Mathematica
    palQ[n_]:= Reverse[x=IntegerDigits[n]] == x; t={}; Do[If[!PrimeQ[n] && And@@palQ/@Join[{n, Total[Times@@@(x=FactorInteger[n])]}, First/@x], AppendTo[t,n]],{n, 2, 3.2*10^6}]; t (* Jayanta Basu, Jun 05 2013 *)

Formula

A046355 INTERSECT A002113. - R. J. Mathar, Sep 09 2015

A046366 Composite numbers divisible by the palindromic sum of their palindromic prime factors (counted with multiplicity).

Original entry on oeis.org

4, 16, 27, 308, 440, 528, 594, 5445, 5808, 6534, 8085, 9702, 11550, 13860, 14784, 16500, 16632, 18711, 19800, 21120, 22275, 23760, 25344, 26730, 28512, 32076, 37268, 53240, 63888, 94864, 135520, 152460, 162624, 181500, 182952, 193600
Offset: 1

Views

Author

Patrick De Geest, Jun 15 1998

Keywords

Comments

The subsequence of numbers k of A046355 such that A262049(k) divides k. - R. J. Mathar, Sep 09 2015

Examples

			1041714 = 2 * 3^3 * 101 * 191 -> Sum of factors is 303 -> 1041714 / 303 = 3438 exactly.

Links

Crossrefs

Cf. A046367.

Programs

  • Maple
    isA046366 := proc(n)
    local sofpp ;
    if isA046355(n) then
        sofpp := A262049(n) ;
        if modp(n,sofpp) = 0 then
            true;
        else
            false;
        end if;
    else
        false;
    end if;
end proc:
for n from 2 to 1000 do
    if isA046366(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[4,10^5],!PrimeQ[#]&&And@@palQ/@Join[{y=Total[Times@@@(x=FactorInteger[#])]},First/@x]&&IntegerQ[#/y]&](* Jayanta Basu, Jun 05 2013 *)

A327749 Natural numbers whose sum of prime factors (with repetition) is palindromic in base 10.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 18, 20, 24, 27, 28, 40, 45, 48, 54, 57, 62, 85, 101, 102, 106, 116, 121, 123, 131, 151, 181, 182, 191, 194, 218, 259, 260, 278, 292, 298, 305, 308, 312, 313, 351, 353, 358, 366, 370, 373, 383, 388, 403, 413, 415, 428, 440, 444, 483, 495, 498
Offset: 1

Views

Author

Robert Bilinski, Sep 23 2019

Keywords

Comments

Union of 1, A046352 and the palindromic primes (A002385). - Corrected by Robert Israel, Nov 20 2020

References

  • Karl G. Kröber, "Palindrome, Perioden und Chaoten: 66 Streifzüge durch die palindromischen Gefilde" (1997, Deutsch-Taschenbücher; Bd. 99) ISBN 3-8171-1522-9.
  • Clifford A. Pickover, A Passion for Mathematics, Wiley, 2005; see p. 71.

Links

Crossrefs

Cf. A001414, A002113, A002385, A046352, A046355.

Programs

  • Magma
    [1] cat [k: k in [2..500]| Intseq(a) eq Reverse(Intseq(a)) where a is &+[m[1]*m[2]: m in Factorization(k)]]; // Marius A. Burtea, Sep 27 2019
  • Maple
    ispali:= proc(n) option remember; local L; L:= convert(n,base,10); evalb(L = ListTools:-Reverse(L)) end proc:
spf:= proc(n) add(t[1]*t[2],t=ifactors(n)[2]) end proc:
select(t -> ispali(spf(t)), [$0..1000]); # Robert Israel, Nov 20 2020
  • Mathematica
    sopfr[1] = 0; sopfr[n_] := Plus @@ (Times @@@ FactorInteger[n]); aQ[n_] := PalindromeQ[sopfr[n]]; Select[Range[500], aQ] (* Amiram Eldar, Sep 23 2019 *)
  • PARI
    sopfr(n) = (n=factor(n))[, 1]~*n[, 2]; \\ A001414
isok(n) = my(d=digits(sopfr(n))); d == Vecrev(d); \\ Michel Marcus, Sep 27 2019
Showing 1-4 of 4 results.

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