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 1-5 of 5 results.

A050697 Numbers that appear in A035140 but not in A050694.

Original entry on oeis.org

121, 132, 143, 187, 295, 312, 341, 351, 451, 671, 679, 781, 928, 932, 1023, 1053, 1057, 1207, 1243, 1255, 1324, 1325, 1328, 1331, 1359, 1375, 1377, 1379, 1392, 1395, 1539, 1573, 1592, 1703, 1775, 1972, 1975, 1982, 2139, 2189, 2317, 2321, 2349, 2367
Offset: 1

Views

Author

Patrick De Geest, Aug 15 1999

Keywords

Comments

Digits of prime factors of a(n) all appear in a(n) but not all prime factors of a(n) are a substring of a(n).

Examples

			187 = 11*17 -> digits 1 and 7 appear in {1}8{7} and 11 and 17 aren't substrings of "187".

Crossrefs

Cf. A050694, A035140.

Programs

  • Mathematica
    d[n_]:=IntegerDigits[n]; t={}; Do[le1=Max@@Length/@(t1=d[First/@FactorInteger[n]]); t2=Flatten[Table[Partition[d[n],i,1],{i,le1}],1]; If[!PrimeQ[n]&&Complement[t1,t2]!={}&&Complement[Flatten[t1],d[n]]=={},AppendTo[t,n]],{n,20,2380}]; t (* Jayanta Basu, May 31 2013 *)

A096593 Erroneous version of A050694.

Original entry on oeis.org

135, 175, 250, 324, 375, 432, 735, 875, 1250, 1352, 1372, 1593, 1675, 1715, 1792
Offset: 1

Views

Author

Keywords

A050695 Composite numbers k such that none of the prime factors of k is a substring of k.

Original entry on oeis.org

4, 6, 8, 9, 10, 14, 16, 18, 21, 27, 34, 38, 40, 44, 46, 48, 49, 51, 54, 56, 57, 58, 60, 64, 66, 68, 69, 74, 76, 78, 80, 81, 84, 86, 87, 88, 90, 91, 94, 96, 98, 99, 100, 104, 106, 108, 111, 114, 116, 117, 118, 119, 121, 129, 133, 134, 136, 140, 141, 143, 144, 146
Offset: 1

Views

Author

Patrick De Geest, Aug 15 1999

Keywords

Comments

A131929(a(n)) = 0; together with 1, complement of A131930. - Reinhard Zumkeller, Jul 30 2007

Examples

			114 = 2*3*19.

Links

Crossrefs

Cf. A050694, A050696, A035139, A050698.

Programs

  • Mathematica
    d[n_]:=IntegerDigits[n]; t={}; Do[le1=Max@@Length/@(t1=d[First/@FactorInteger[n]]); t2=Flatten[Table[Partition[d[n],i,1],{i,le1}],1]; If[!PrimeQ[n]&&Intersection[t1,t2]=={},AppendTo[t,n]],{n,2,146}]; t (* Jayanta Basu, May 31 2013 *)
npfsQ[n_]:=Module[{idn=IntegerDigits[n],f=FactorInteger[n][[All,1]]}, And@@ Table[SequenceCount[idn,IntegerDigits[f[[i]]]]==0,{i, Length[ f]}]]; Select[Range[200],CompositeQ[#] && npfsQ[#]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Dec 28 2016 *)

A050696 At least one prime factor of composite a(n) is a substring of a(n).

Original entry on oeis.org

12, 15, 20, 22, 24, 25, 26, 28, 30, 32, 33, 35, 36, 39, 42, 45, 50, 52, 55, 62, 63, 65, 70, 72, 75, 77, 82, 85, 92, 93, 95, 102, 105, 110, 112, 115, 120, 122, 123, 124, 125, 126, 128, 130, 132, 135, 138, 142, 145, 147, 150, 152, 153, 155, 162, 165, 170, 172, 175
Offset: 1

Views

Author

Patrick De Geest, Aug 15 1999

Keywords

Examples

			26 is in the sequence because 26 = 2 * 13 and the factor 2 appears in the decimal representation. Though 13 does not appear, the 2 is enough for 26 to be in the sequence.
27 is not in the sequence since 27 = 3 * 3 * 3, which does not appear in the decimal representation.

Links

Crossrefs

Cf. A050694, A050695.

Programs

  • Mathematica
    digs[n_] := IntegerDigits[n]; A050696 = {}; Do[le1 = Max@@Length/@(prFDigs = digs[First/@FactorInteger[n]]); dSubStrs = Flatten[Table[Partition[digs[n], i, 1], {i, le1}], 1]; If[!PrimeQ[n] && Intersection[prFDigs, dSubStrs] != {}, AppendTo[A050696, n]],{n, 2, 180}]; A050696 (* Jayanta Basu, May 31 2013 *)

A059401 Numbers that contain as proper substrings every maximal prime power dividing them.

Original entry on oeis.org

1197, 2510, 2570, 5210, 5230, 5290, 12590, 14673, 15230, 20530, 21530, 22510, 23510, 23570, 24590, 25030, 25210, 25310, 25390, 25430, 25490, 25510, 25570, 25790, 25910, 25930, 26570, 26590, 27530, 28510, 28570, 29530, 29570, 32510
Offset: 1

Views

Author

Erich Friedman, Jan 29 2001

Keywords

Comments

Most terms end in 0, since 2*5*prime will work if prime contains 2 and 5 as substrings. The other terms are listed in A059402.
There must be at least two maximal prime powers dividing each term. - Harvey P. Dale, Dec 04 2016

Examples

			1197 = 9 * 7 * 19 and all of these are substrings.

Links

Crossrefs

Cf. A141809, A010055.
Subsequence of A024619.
A059402 is a subsequence.
Equivalent sequence for primes instead of maximal prime powers: A050694.

Programs

  • Haskell
    import Data.List (isInfixOf)
a059401 n = a059401_list !! (n-1)
a059401_list = filter (\x -> a010055 x == 0 &&
               all (`isInfixOf` show x) (map show $ a141809_row x)) [1..]
-- Reinhard Zumkeller, Dec 16 2013
  • Mathematica
    psmppQ[n_]:=Module[{pp=#[[1]]^#[[2]]&/@FactorInteger[n], idn= IntegerDigits[ n]}, Length[pp]>1&&And@@Table[ SequenceCount[ idn, IntegerDigits[pp[[i]]]]>0,{i,Length[pp]}]]; Select[Range[ 33000], psmppQ] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Dec 04 2016 *)

Extensions

Offset corrected by Reinhard Zumkeller, Dec 16 2013
Edited by Peter Munn, Sep 01 2022
Showing 1-5 of 5 results.

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

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