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.

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

A089317 Prime worms [successive digit differences with absolute value of 4].

Original entry on oeis.org

151, 373, 95959, 9515959, 159595151, 159595951, 15151595951, 15951595151, 95951515159, 1515159515951, 1515959515951, 1515959595151, 1595159515151, 1595159595151, 9515151515159, 9515159515159, 9515159595959, 9595159515959
Offset: 0

Views

Author

Enoch Haga, Dec 25 2003

Keywords

Examples

			a(1)=373; first and last digits are 3; abs(3-7)=4; abs(7-3)=4; the worm is 3.

References

  • Carlos Rivera's primepuzzles.net, Puzzle 246

Links

Crossrefs

This is a subsequence of A048401. Cf. A089291, A089315-A089316, A048398-A048405.

Formula

Select prime numbers having the same first and last digits; if the uniform absolute value of successive digit differences is 4, add to sequence.

Extensions

More terms from David Wasserman, Sep 09 2005

A089316 Prime worms [successive digit differences with absolute value of 2].

Original entry on oeis.org

131, 313, 353, 757, 797, 35353, 35753, 75797, 79757, 97579, 3131353, 3135313, 3531313, 7535797, 313131353, 313135313, 313579753, 353535313, 357531313, 357531353, 357535753, 357575753, 357975353, 753535357, 757975357, 975353579
Offset: 0

Views

Author

Enoch Haga, Dec 25 2003

Keywords

Examples

			a(4)=797; first and last digits are 7; abs(7-9)=2; abs(9-7)=2; the worm is 7.

Links

Crossrefs

Cf. A089291.
This is a subset of A048399. Cf. A089291, A089315, A089317, A048398-A048405.

Programs

  • Mathematica
    pwQ[n_]:=Module[{idn=IntegerDigits[n]},First[idn]==Last[idn]&&Union[Abs[ Differences[idn]]]=={2}]; Select[Prime[Range[50000000]],pwQ] (* Harvey P. Dale, Mar 26 2013 *)

Formula

Select prime numbers having the same first and last digits; if the uniform absolute value of successive digit differences is 2, add to sequence.

A089360 Prime worms.

Original entry on oeis.org

101, 131, 151, 181, 191, 313, 353, 373, 383, 727, 757, 787, 797, 919, 929, 12101, 14741, 18181, 32323, 34543, 35353, 35753, 72727, 74747, 75797, 78787, 79757, 94949, 95959, 97579, 1012321, 1212121, 1414741, 1474141, 1616161, 3131353
Offset: 1

Views

Author

Enoch Haga, Dec 27 2003

Keywords

Comments

While some palindromic primes are included, there are other criteria for addition to this sequence.

Examples

			a(15)=12101; first and last digits = 1; no identical adjacent digits; abs(1-2)=1;abs(2-1)=1; abs(1-0)=1; abs(0-1)=1; the worm is 1.

References

  • Carlos Rivera's primepuzzles.net, Puzzle 246

Links

Crossrefs

Cf. A089291, A089315-89317, A048398-48405.

Formula

From sequence of primes beginning with 3-digits, select those with identical first and last digits; no adjacent digits identical; and absolute value of sequential differences of paired digits a constant.
Showing 1-4 of 4 results.

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

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