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.

A046510 Numbers with multiplicative persistence value 1.

Original entry on oeis.org

10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 30, 31, 32, 33, 40, 41, 42, 50, 51, 60, 61, 70, 71, 80, 81, 90, 91, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 130, 131, 132, 133
Offset: 1

Views

Author

Patrick De Geest, Sep 15 1998

Keywords

Comments

Numbers 0 to 9 have a multiplication persistence of 0, not 1. - Daniel Mondot, Mar 12 2022

Examples

			24 -> 2 * 4 = [ 8 ] -> one digit in one step.

Links

Crossrefs

Cf. A003001, A014120, A046501.
Numbers with multiplicative persistence m: this sequence (m=1), A046511 (m=2), A046512 (m=3), A046513 (m=4), A046514 (m=5), A046515 (m=6), A046516 (m=7), A046517 (m=8), A046518 (m=9), A352531 (m=10), A352532 (m=11).

Programs

  • Mathematica
    Select[Range[10, 121], IntegerLength[Times @@ IntegerDigits[#]] <= 1 &] (* Jayanta Basu, Jun 26 2013 *)
  • PARI
    isok(n) = my(d=digits(n)); (#d > 1) && (#digits(prod(k=1, #d, d[k])) <= 1); \\ Michel Marcus, Apr 12 2018 and Mar 13 2022
  • Python
    from math import prod
def ok(n): return n > 9 and prod(map(int, str(n))) < 10
print([k for k in range(134) if ok(k)]) # Michael S. Branicky, Mar 13 2022

Extensions

Incorrect terms 0 to 9 removed by Daniel Mondot, Mar 12 2022

A159613 Palindromic primes with multiplicative persistence value 1.

Original entry on oeis.org

11, 101, 131, 151, 181, 191, 313, 10301, 10501, 10601, 11311, 11411, 16061, 30103, 30203, 30403, 30703, 30803, 31013, 35053, 38083, 70207, 70507, 70607, 73037, 74047, 90709, 91019, 94049, 1003001, 1008001, 1022201, 1028201, 1035301
Offset: 1

Views

Author

Lekraj Beedassy, Apr 17 2009

Keywords

Links

Crossrefs

Cf. A046501.
Cf. A056709. - R. J. Mathar, Apr 21 2009

Programs

  • Maple
    isA002113 := proc(n) local dgs,i ; dgs := convert(n,base,10) ; for i from 1 to nops(dgs)/2 do if op(i,dgs) <> op(-i,dgs) then RETURN(false): fi; od: RETURN(true) ; end: ndigs := proc(n) max(1, ilog10(n)+1) ; end: A031346 := proc(n) local p,nred; p := 0 ; nred := n ; while ndigs(nred) > 1 do nred := mul(d, d=convert(nred,base,10) ) ; p := p+1 ; od: p ; end: isA159613 := proc(n) RETURN(isprime(n) and isA002113(n) and A031346(n) = 1) ; end: for n from 1 to 100000 do p := ithprime(n) ; if isA159613(p) then printf("%d,",p) ; fi; od: # R. J. Mathar, Apr 21 2009
  • Mathematica
    palpQ[n_]:=Module[{idn=IntegerDigits[n]},idn==Reverse[idn] && Length[ NestWhileList[Times@@IntegerDigits[#]&,n,#>9&]]==2]; Select[Prime[ Range[82000]],palpQ] (* Harvey P. Dale, Dec 16 2011 *)

Formula

A002385 INTERSECT A046501. - R. J. Mathar, Apr 21 2009

Extensions

Extended by R. J. Mathar, Apr 21 2009

A159614 Emirps with multiplicative persistence value 1.

Original entry on oeis.org

13, 17, 31, 71, 107, 113, 311, 701, 709, 907, 1009, 1021, 1031, 1033, 1061, 1069, 1091, 1097, 1103, 1109, 1151, 1181, 1201, 1213, 1231, 1301, 1321, 1409, 1511, 1601, 1811, 1901, 3011, 3019, 3023, 3049, 3067, 3083, 3089, 3109, 3121, 3203, 3301, 3407, 3803
Offset: 1

Views

Author

Lekraj Beedassy, Apr 17 2009

Keywords

Comments

Intersection of A006567 and A046501.

Crossrefs

Cf. A006567, A046501.

Programs

  • Maple
    read("transforms3") ; A031346 := proc(n) local nm,a,d ; nm := n ; a := 0 ; while nm > 10 do nm := mul(d,d=convert(nm,base,10)) ; a := a+1: od: a ; end: L := BFILETOLIST("b006567.txt") : for i from 1 to 300 do if A031346(op(i,L)) = 1 then printf("%d,", op(i,L)) ; fi; od: # R. J. Mathar, Apr 29 2009

Extensions

More terms from R. J. Mathar, Apr 29 2009

A199991 Nonprime numbers whose multiplicative persistence is 1.

Original entry on oeis.org

10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 30, 32, 33, 40, 42, 50, 51, 60, 70, 80, 81, 90, 91, 100, 102, 104, 105, 106, 108, 110, 111, 112, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 130, 132, 133, 140, 141, 142, 150, 160, 161, 170, 171, 180, 190
Offset: 1

Views

Author

Jaroslav Krizek, Nov 13 2011

Keywords

Comments

Complement of A046501 with respect to A046510.

Examples

			105 -> 1 * 0 * 5 = 0; one digit in one step.

Crossrefs

Cf. A046501 (primes whose multiplicative persistence is 1).

Programs

  • Mathematica
    persistence[n_] := Module[{cnt = 0, k = n}, While[k > 9, cnt++; k = Times @@ IntegerDigits[k]]; cnt]; Select[Range[200], ! PrimeQ[#] && persistence[#] == 1 &] (* T. D. Noe, Nov 23 2011 *)
Showing 1-4 of 4 results.

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