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 1-3 of 3 results.

A089291 Prime worms (as defined below).

Original entry on oeis.org

101, 787, 12101, 32323, 34543, 78787, 1012321, 1212121, 3212123, 3212323, 3454343, 7654567, 7656787, 7676567, 7678787, 7876567, 7898767, 101012321, 101210101, 101232121, 121232101, 123210121, 123232121, 321234343, 323232323
Offset: 1

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Author

Enoch Haga, Dec 23 2003

Keywords

Comments

By analogy, primes of this type are worms with a head and tail and body composed of the same digit which weaves in and out of the prime. In a(2)=12101 the worm is defined by the digit 1.

Examples

			a(2)=12101 because that number is prime with identical first and last digits. Then abs(1-2)=1; abs(2-1)=1; abs(1-0)=1; abs(0-1)=1; and sum of absolute values is 4, one less than the 5 digits in the prime.

References

  • The concept is due to Carlos Rivera in his Puzzle 246 (where he asks for the first pandigital prime worm and for the first pandigital titanic prime worm - solutions are at his site).

Links

Crossrefs

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

Formula

Primes whose first and last digits are identical and whose successive digit differences have a uniformly absolute value of 1. Thus the sum of absolute values is one less than the number of digits in the prime. No two adjacent digits are identical or differ by more than one.

Extensions

Edited by Charles R Greathouse IV, Aug 02 2010

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

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.
Showing 1-3 of 3 results.

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

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