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 1-6 of 6 results.

A051018 Numbers that are 2-persistent but not 3-persistent.

Original entry on oeis.org

1023456789, 1023456879, 1023457689, 1023457869, 1023458679, 1023458769, 1023465789, 1023465879, 1023467589, 1023467859, 1023468579, 1023468759, 1023475689, 1023475869, 1023476589, 1023476859, 1023478569, 1023478659, 1023485679, 1023485769, 1023486579, 1023486759
Offset: 1

Views

Author

Eric W. Weisstein

Keywords

Comments

A number m is k-persistent iff all of {m, 2m,..., km} are pandigital (in the sense of A171102).

Links

Crossrefs

Cf. A171102 (pandigital), A204047 (smallest n-persistent), A051264 (1-persistent), A051019 (3-persistent), A051020 (4-persistent), A204096 (5-persistent), A204097 (6-persistent).

Programs

  • PARI
    is_A051018(n,k=3)=10>#Set(Vec(Str(k*n))) & !while(k--,9<#Set(Vec(Str(k*n))) || return(0)) \\ M. F. Hasler, Jan 10 2012

Extensions

Definition corrected by Franklin T. Adams-Watters, Jan 09 2012

A051019 Numbers that are 3-persistent but not 4-persistent.

Original entry on oeis.org

1052674893, 1052687493, 1052746893, 1052748693, 1052867493, 1052874693, 1053267489, 1053268749, 1053274869, 1053286749, 1053287469, 1065273489, 1065287349, 1067285493, 1067328549, 1068547293, 1068547329, 1068549273
Offset: 1

Views

Author

Eric W. Weisstein

Keywords

Comments

A number n is k-persistent iff all of {n, 2n,..., kn} are pandigital (in the sense of A171102).

Links

Crossrefs

Cf. A171102 (pandigital), A204047 (smallest n-persistent), A051264 (1-persistent), A051018 (2-persistent), A051020 (4-persistent), A204096 (5-persistent), A204097 (6-persistent).

Programs

  • PARI
    is_A051019(n)=for(i=1,4, 9<#Set(Vec(Str(i*n))) || return(i>3)) \\ M. F. Hasler, Jan 10 2012

Extensions

Definition corrected by Franklin T. Adams-Watters, Jan 09 2012

A051020 Numbers that are 4-persistent but not 5-persistent.

Original entry on oeis.org

1053274689, 1089467253, 1253094867, 1267085493, 1268547309, 1269085473, 1273085469, 1308547269, 1308549267, 1326854907, 1327068549, 1328746905, 1450687329, 1450732869, 1450867293, 1450928673, 1452687309, 1452690873
Offset: 1

Views

Author

Eric W. Weisstein

Keywords

Comments

A number n is k-persistent iff all of {n, 2*n, ..., k*n} are pandigital (in the sense of A171102).

Links

Crossrefs

Cf. A171102 (pandigital), A204047 (smallest n-persistent), A051264 (1-persistent), A051018 (2-persistent), A051019 (3-persistent), A204096 (5-persistent), A204097 (6-persistent).

Programs

  • PARI
    is_A051020(n)=for(i=1, 5, 9<#Set(Vec(Str(i*n))) || return(i>4)) \\ M. F. Hasler, Jan 10 2012

Extensions

Definition corrected by Franklin T. Adams-Watters, Jan 09 2012
Sequence corrected by Hans Havermann, Jan 11 2012

A051264 Numbers that are 1-persistent but not 2-persistent.

Original entry on oeis.org

1023456798, 1023456897, 1023456978, 1023456987, 1023457698, 1023457896, 1023457968, 1023457986, 1023458697, 1023458796, 1023458967, 1023458976, 1023459678, 1023459687, 1023459768, 1023459786, 1023459867, 1023459876
Offset: 1

Views

Author

Eric W. Weisstein

Keywords

Comments

A number n is k-persistent iff all of {n, 2n,..., kn} are pandigital (in the sense of A171102).

Links

Crossrefs

Cf. A171102 (1-persistent, i.e. pandigital numbers), A204047 (smallest n-persistent), A051018 (2-persistent), A051019 (3-persistent), A051020 (4-persistent), A204096 (5-persistent), A204097 (6-persistent).

Formula

A051264 = A171102 \ A051018. - M. F. Hasler, Jan 09 2012

Extensions

Definition corrected by Franklin T. Adams-Watters, Jan 09 2012

A204047 Smallest number that is n-persistent but not (n+1)-persistent, i.e., k, 2k, ..., nk, but not (n+1)k, are pandigital in the sense of A171102; 0 if such a number does not exist.

Original entry on oeis.org

1023456798, 1023456789, 1052674893, 1053274689, 13047685942, 36492195078, 153846076923, 251793406487, 0, 1189658042735, 5128207435967, 3846154076923, 125583660720493, 125583660493072, 180106284973592, 201062849735918
Offset: 1

Views

Author

Hans Havermann, Jan 09 2012

Keywords

Comments

a(9) is 0 because any 9-persistent number is also 10-persistent. Indeed, if n is pandigital, 10*n is pandigital as well.
In the same way, a(10m-1)=0 for all m>0 since if kn is pandigital for all k=1,...,10m-1, then mn is pandigital and so is 10mn. - M. F. Hasler, Jan 10 2012

Examples

			k=36492195078 is the smallest number such that k, 2k, 3k, 4k, 5k, and 6k, each contain all ten digits, but 7k=255445365546 contains only five of the ten, so a(6)= 36492195078.

References

  • Ross Honsberger, More Mathematical Morsels, Mathematical Association of America, 1991, pages 15-18.

Crossrefs

Cf. A051264, A051018, A051019, A051020, A204096, A204097.

Extensions

a(7)-a(16) from Giovanni Resta, Jan 10 2012

A204097 Numbers that are 6-persistent but not 7-persistent.

Original entry on oeis.org

36492195078, 48602175913, 48613021759, 49021758613, 49130217586, 49219635078, 53829197460, 53829301746, 53928301746, 54601738293, 54601739283, 58829301746, 59288301746, 60174538293, 60174539283, 60174588293, 60174592883, 64820935179
Offset: 1

Views

Author

Hans Havermann, Jan 10 2012

Keywords

Comments

A number n is k-persistent iff all of {n, 2n,..., kn} are pandigital (in the sense of A171102).

References

  • Ross Honsberger, More Mathematical Morsels, Mathematical Association of America, 1991, pages 15-18.

Links

Crossrefs

Cf. A171102 (pandigital), A051264 (1-persistent), A051018 (2-persistent), A051019 (3-persistent), A051020 (4-persistent), A204096 (5-persistent), A204047 (smallest n-persistent).
Showing 1-6 of 6 results.

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

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