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 1-7 of 7 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 *)

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 *)

A048403 Primes with consecutive digits that differ exactly by 6.

Original entry on oeis.org

2, 3, 5, 7, 17, 71, 1717171717171717171717171717171, 1717171717171717171717171717171717171
Offset: 1

Views

Author

Patrick De Geest, Apr 15 1999

Keywords

Comments

From Andrew Howroyd, Aug 13 2024: (Start)
Terms with more than 1 digit have digits alternating between 1 and 7.
No more terms < 10^3000. (End)

Crossrefs

Primes in A048408.
Cf. A048398, A048399, A048400, A048401, A048402, A048404, A048405.

Programs

  • PARI
    upto(limit)={my(L=List([t|t<-[2,3,5],t<=limit]),m=1); while(mAndrew Howroyd, Aug 13 2024

Extensions

Offset changed by Andrew Howroyd, Aug 13 2024

A089315 Prime worms [successive digit differences with absolute value of 3].

Original entry on oeis.org

14741, 74747, 1414741, 1474141, 14141414141, 14141414741, 14141474741, 14147414741, 14147474141, 74141414147, 1474741414141, 7474141474747, 7474741414747, 14141474141414141, 14147414747474741, 14147474147474741
Offset: 0

Views

Author

Enoch Haga, Dec 25 2003

Keywords

Comments

One of a family of prime worms differing according to the uniform absolute value of successive digit pairs. Sequence checked to 10^9.
This is a subset of A048400. Cf. A089291, A089316-A089317, A048398-A048405.

Examples

			a(1)=74747 because the number is prime, has identical first and last digits and abs(7-4)=3; abs(4-7)=3; abs(7-4)=3 and abs(4-7)=3. In this number, the worm is 7.

References

  • Carlos Rivera's primepuzzles.net, Puzzle 246.

Links

Formula

Select prime numbers having the same first and last digits; if the uniform absolute value of successive digit differences is 3, add to sequence.

Extensions

More terms from David Wasserman, Sep 09 2005
Showing 1-7 of 7 results.

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

Content is available under The OEIS End-User License Agreement.