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.

A048405 Primes with consecutive digits that differ exactly by 8.

Original entry on oeis.org

2, 3, 5, 7, 19, 191, 919, 919191919, 91919191919, 91919191919191919, 91919191919191919191919, 191919191919191919191919191919191
Offset: 1

Views

Author

Patrick De Geest, Apr 15 1999

Keywords

Comments

The next term (a(13)) has 133 digits. - Harvey P. Dale, Jan 04 2023

Examples

			2 is a term since all its consecutive digits differ by 5 (there aren't any).
19 is a term because 1 and 9 differ by 8.
23 is not a term because its consecutive digits differ only by 1.

Links

Crossrefs

Cf. A048398, A048399, A048400, A048401, A048402, A048403, A048404, A048410.

Programs

  • Mathematica
    Module[{nn=500,nine,one},one=Select[Table[FromDigits[PadRight[{},n,{1,9}]],{n,nn}],PrimeQ];nine=Select[Table[FromDigits[PadRight[{},n,{9,1}]],{n,nn}],PrimeQ];Sort[Join[{2,3,5,7},nine,one]]] (* Harvey P. Dale, Jan 04 2023 *)

Extensions

Offset corrected by Sean A. Irvine, Jun 16 2021

A048399 Primes with consecutive digits that differ exactly by 2.

Original entry on oeis.org

2, 3, 5, 7, 13, 31, 53, 79, 97, 131, 313, 353, 757, 797, 31357, 35353, 35753, 35797, 75353, 75797, 79757, 97579, 131357, 135353, 135757, 353531, 531353, 535757, 575753, 579757, 757579, 797579, 975313, 975797, 979757, 1313579, 3131353
Offset: 1

Views

Author

Patrick De Geest, Apr 15 1999

Keywords

Links

Crossrefs

Cf. A033088, A048398, A048400, A048401, A048402, A048403, A048404, A048405.

Programs

  • Mathematica
    Join[{2,3,5,7},Select[Prime[Range[230000]],Union[Abs[ Differences[ IntegerDigits[ #]]]]=={2}&]] (* Harvey P. Dale, Nov 03 2013 *)

A048400 Primes with consecutive digits that differ exactly by 3.

Original entry on oeis.org

2, 3, 5, 7, 41, 47, 14741, 14747, 74747, 1414741, 1474141, 7414741, 4141414747, 4147414147, 14141414141, 14141414741, 14141474741, 14141474747, 14147414741, 14147474141, 14147474147, 14741414747, 74141414147, 74141414741, 74147414741, 74741474741, 74747414141
Offset: 1

Views

Author

Patrick De Geest, Apr 15 1999

Keywords

Comments

All terms with more than a single digit must comprise only the digits 1, 4, and 7, because no number comprising the digits 2, 5, and 8 or the digits 3, 6, and 9 can be prime. - Harvey P. Dale, Mar 01 2023

Links

Crossrefs

Cf. A033081, A048398, A048399, A048401, A048402, A048403, A048404, A048405.

Programs

  • Mathematica
    Join[{2,3,5,7},Table[Select[FromDigits/@Tuples[{1,4,7},n],PrimeQ[#]&& Union[ Abs[ Differences[ IntegerDigits[ #]]]]=={3}&],{n,11}]//Flatten] (* Harvey P. Dale, Mar 01 2023 *)

Extensions

More terms from Naohiro Nomoto, Jul 28 2001
More terms from Sean A. Irvine, Jun 15 2021

A048401 Primes with consecutive digits that differ exactly by 4.

Original entry on oeis.org

2, 3, 5, 7, 37, 59, 73, 151, 373, 15959, 95959, 515951, 595159, 595951, 9515959, 51515159, 159595151, 159595951, 5151515951, 5159515159, 5159515951, 5951515151, 5951515951, 5959515151, 5959595951, 15151595951, 15951515159
Offset: 1

Views

Author

Patrick De Geest, Apr 15 1999

Keywords

Links

Crossrefs

Cf. A048398, A048399, A048400, A048402, A048403, A048404, A048405, A048406.

Programs

  • Mathematica
    pd[{a_,b_,c___}]:=Flatten[Table[Select[FromDigits/@Select[Tuples[ {a,b,c},n],Union[Abs[Differences[#]]]=={4}&],PrimeQ],{n,11}]]; Union[Join[{2,3,5,7},pd[{1,5,9}],pd[{3,7}]]] (* Harvey P. Dale, Aug 23 2011 *)

Extensions

More terms from Naohiro Nomoto, Jul 28 2001

A048402 Primes with consecutive digits that differ exactly by 5.

Original entry on oeis.org

2, 3, 5, 7, 61, 83, 383, 727, 72727, 94949, 1616161, 383838383, 727272727, 383838383838383, 38383838383838383, 72727272727272727, 94949494949494949, 383838383838383838383
Offset: 1

Views

Author

Patrick De Geest, Apr 15 1999

Keywords

Links

Crossrefs

Cf. A048398, A048399, A048400, A048401, A048403, A048404, A048405, A048407.

Programs

  • Mathematica
    Module[{nn=50,w1,w2},w1=Flatten[Table[Select[FromDigits/@Table[ PadRight[ {},n,{a,a+5}],{n,2,nn}],PrimeQ],{a,4}]];w2=Flatten[Table[Select[ FromDigits/@ Table[PadRight[{},n,{a+5,a}],{n,2,nn}],PrimeQ],{a,4}]];Join[ {2,3,5,7},w1,w2]//Union] (* Harvey P. Dale, Jan 09 2021 *)

A048404 Primes with consecutive digits that differ exactly by 7.

Original entry on oeis.org

2, 3, 5, 7, 29, 181, 929, 18181, 929292929, 18181818181818181818181818181818181818181818181818181818181818181818181818181
Offset: 1

Views

Author

Patrick De Geest, Apr 15 1999

Keywords

Comments

The next term (a(11)) has 163 digits. - Harvey P. Dale, Mar 23 2023

Links

Crossrefs

Cf. A048398, A048399, A048400, A048401, A048402, A048403, A048405, A048409.

Programs

  • Mathematica
    Module[{s18,s81,s29,s92},s18=Select[Table[FromDigits[PadRight[{},n,{1,8}]],{n,1,181,2}],PrimeQ]; s81=Select[Table[FromDigits[PadRight[{},n,{8,1}]],{n,2,182,2}],PrimeQ];s29 = Select[ Table[FromDigits[PadRight[{},n,{2,9}]],{n,2,182,2}],PrimeQ]; s92 =Select[Table[ FromDigits[ PadRight[{},n,{9,2}]],{n,1,183,2}],PrimeQ]; Join[{2,3,5,7},s18,s81,s29,s92]//Sort] (* Harvey P. Dale, Mar 23 2023 *)
Showing 1-6 of 6 results.

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