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 1-3 of 3 results.

A050700 Composite numbers n smaller than their decimal reverse but having the same number of prime factors.

Original entry on oeis.org

15, 26, 39, 49, 58, 115, 117, 122, 123, 126, 129, 143, 147, 155, 158, 159, 165, 169, 177, 178, 183, 185, 187, 203, 205, 225, 226, 244, 246, 265, 285, 286, 289, 294, 314, 315, 319, 326, 327, 329, 335, 338, 339, 355, 366, 369, 394, 398, 406, 415, 418, 425
Offset: 1

Views

Author

Patrick De Geest, Aug 15 1999

Keywords

Examples

			a(n)=143 -> a(n)-reversed=341 gives pair (143,341) of which only the smaller value 143 is in this sequence.

Links

Crossrefs

Cf. A050699, A050701.

Programs

  • Mathematica
    rev[n_]:=FromDigits[Reverse[IntegerDigits[n]]]; Select[Range[425],!PrimeQ[#]&&PrimeOmega[#]==PrimeOmega[x=rev[#]]&&#Jayanta Basu, May 31 2013 *)
  • PARI
    is(n)=my(r=fromdigits(Vecrev(digits(n)))); nCharles R Greathouse IV, Oct 17 2018

Extensions

Name edited and offset corrected by Charles R Greathouse IV, Oct 17 2018

A050701 If composite k and its reverse are different and have same number of prime factors, then the larger of them is a term of the sequence.

Original entry on oeis.org

51, 62, 85, 93, 94, 221, 302, 321, 341, 381, 413, 442, 492, 493, 502, 511, 513, 514, 522, 524, 533, 534, 551, 553, 561, 562, 574, 581, 582, 604, 605, 621, 622, 623, 642, 663, 682, 685, 705, 711, 723, 734, 741, 766, 771, 781, 794, 805, 814, 817
Offset: 1

Views

Author

Patrick De Geest, Aug 15 1999

Keywords

Examples

			a(n)=341 -> reverse(a(n)) = 143 gives the pair (143,341) of which only the larger value 341 is retained.

Crossrefs

Cf. A004086, A050699, A050700.

Programs

  • Mathematica
    rev[n_]:=FromDigits[Reverse[IntegerDigits[n]]]; Select[Range[825],!PrimeQ[#]&&PrimeOmega[#]==PrimeOmega[x=rev[#]]&&#>x&] (* Jayanta Basu, May 31 2013 *)
  • PARI
    isok(m) = my(k=fromdigits(Vecrev(digits(m)))); (m%10) && !isprime(m) && (m>k) && (bigomega(k) == bigomega(m)); \\ Michel Marcus, Aug 18 2021

Extensions

Revised by Editors of OEIS, Oct 19 2019
Incorrect 394 and 523 removed and name clarified by Sean A. Irvine, Aug 17 2021

A050702 Nonprime numbers n such that n and n-reversed (<>n and no leading zeros) have the same number of prime factors and these prime factors (palindromes allowed here) are also reversals of each other.

Original entry on oeis.org

26, 39, 62, 93, 143, 169, 187, 226, 286, 339, 341, 622, 682, 781, 933, 961, 1089, 1177, 1243, 1313, 1469, 1573, 1717, 2042, 2062, 2066, 2178, 2206, 2402, 2426, 2446, 2462, 2486, 2602, 2626, 2642, 3063, 3093, 3099, 3131, 3309, 3421, 3603, 3639, 3669, 3693, 3737, 3751, 3903, 3939, 3963, 4084
Offset: 1

Views

Author

Patrick De Geest, Aug 15 1999

Keywords

Comments

Prime factors counted without multiplicity. - Harvey P. Dale, Nov 29 2014

Examples

			Reversing 339 = 3*113 gives 933 = 3*311, both with two prime factors.

Links

Crossrefs

Cf. A050699.

Programs

  • Mathematica
    d[n_]:=IntegerDigits[n]; f[n_]:=First/@FactorInteger[n]; Select[Range[4100],!PrimeQ[#]&&Reverse/@d[f[#]]==d[f[x=FromDigits[Reverse[d[#]]]]]&&#!=x&](* Jayanta Basu, May 31 2013 *)
snpfQ[n_]:=Module[{pfn=Transpose[FactorInteger[n]][[1]],idn = IntegerDigits[ n], revn, pfrev, revpfrev},revn = FromDigits[ Reverse[idn]];pfrev=Transpose[ FactorInteger[ revn]][[1]]; revpfrev =FromDigits[Reverse[IntegerDigits[#]]]&/@pfrev;!PrimeQ[n]&& Last[ IntegerDigits[ n]] != 0&&revn!=n&&Length[pfn]==Length[pfrev]&&Union[pfn] == Union[ revpfrev]]; Select[ Range[ 4200], snpfQ] (* Harvey P. Dale, Nov 29 2014 *)

Extensions

More terms from Naohiro Nomoto, Apr 03 2001
Corrected by Vincenzo Librandi, Feb 03 2014
Definition clarified by Harvey P. Dale, Nov 29 2014
Showing 1-3 of 3 results.

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

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