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 1-5 of 5 results.

A238057 Primes which are the concatenation of two primes in exactly two ways.

Original entry on oeis.org

313, 317, 373, 797, 1373, 1913, 1973, 1997, 2113, 2293, 2311, 2347, 2383, 2389, 2953, 2971, 3167, 3313, 3373, 3593, 3673, 3677, 3719, 3733, 3761, 4337, 4397, 5233, 5347, 5953, 6173, 6197, 6737, 7193, 7331, 7433, 7577, 7877, 7919, 7937, 10313, 10337, 10937
Offset: 1

Views

Author

Colin Barker, Feb 17 2014

Keywords

Examples

			313 is in the sequence because 31 and 3 are both primes, and 3 and 13 are both primes, so there are two ways.

Links

Crossrefs

Cf. A105184, A238056.
Cf. A010051, A000040.

Programs

  • Haskell
    a238057 n = a238057_list !! (n-1)
a238057_list = filter ((== 2) . length . f) a000040_list where
  f x = filter (\(us, vs) ->
               head vs /= '0' &&
               a010051' (read us :: Integer) == 1 &&
               a010051' (read vs :: Integer) == 1) $
               map (flip splitAt $ show x) [1 .. length (show x) - 1]
-- Reinhard Zumkeller, Feb 27 2014
  • Mathematica
    spl[n_] := Block[{d = IntegerDigits@n, c = 0, z}, z = Length@d; Do[ If[ PrimeQ@ FromDigits@ Take[d, k] && d[[k + 1]] > 0 && PrimeQ@ FromDigits@ Take[d, k - z], c++], {k, z - 1}]; c]; Select[ Prime@ Range@1400, spl[#] == 2 &] (* Giovanni Resta, Feb 27 2014 *)

A129800 Prime numbers that can be written as the concatenation of two other prime numbers in exactly one way.

Original entry on oeis.org

23, 37, 53, 73, 113, 137, 173, 193, 197, 211, 223, 229, 233, 241, 271, 283, 293, 307, 311, 331, 337, 347, 353, 359, 367, 379, 383, 389, 397, 433, 503, 523, 541, 547, 571, 593, 613, 617, 673, 677, 719, 733, 743, 761, 773, 977, 1013, 1033, 1093, 1097, 1103
Offset: 1

Views

Author

Pierre CAMI, Jun 03 2007

Keywords

Examples

			113 is a prime number and the concatenation of two prime numbers: (11)(3). This decomposition is unique because (1)(13) is not valid since 1 is not a prime.
However 313 can be seen as both (31)(3) and (3)(13), hence there is no unique decomposition and 313 is not in the sequence.

Links

Crossrefs

Cf. A238056, A010051, A000040.

Programs

  • Haskell
    a129800 n = a129800_list !! (n-1)
a129800_list = filter ((== 1) . length . f) a000040_list where
  f x = filter (\(us, vs) ->
               a010051' (read us :: Integer) == 1 &&
               a010051' (read vs :: Integer) == 1) $
               map (flip splitAt $ show x) [1 .. length (show x) - 1]
-- Reinhard Zumkeller, Feb 27 2014
  • Mathematica
    a = {}; For[n = 5, n < 200, n++, b = IntegerDigits[Prime[n]]; in = 0; For[j = 1, j < Length[b], j++, If[PrimeQ[FromDigits[Take[b, j]]] && PrimeQ[FromDigits[Drop[ b, j]]], in++ ]]; If[in == 1, AppendTo[a, Prime[n]]]]; a (* Stefan Steinerberger, Jun 04 2007 *)

Extensions

More terms from Stefan Steinerberger, Jun 04 2007

A238499 Primes which are the concatenation of two primes in exactly three ways.

Original entry on oeis.org

3137, 3797, 13997, 19937, 19997, 23911, 23929, 29173, 29311, 31193, 37337, 37397, 43397, 59929, 73331, 78737, 79337, 103997, 109397, 127997, 139967, 173347, 173359, 193337, 193373, 193877, 199337, 199373, 199967, 229373, 233113, 233329, 233353, 233617
Offset: 1

Views

Author

Colin Barker, Feb 27 2014

Keywords

Examples

			13997 is in the sequence because (13, 997), (139, 97), (1399, 7) are all primes, so there are three ways.

Links

Crossrefs

Cf. A105184, A238056, A238057, A238500.

Programs

  • Mathematica
    spl[n_] := Block[{d = IntegerDigits@n, c = 0, z}, z = Length@d; Do[If[PrimeQ@ FromDigits@ Take[d, k] && d[[k + 1]] > 0 && PrimeQ@ FromDigits@ Take[d, k - z], c++], {k, z - 1}]; c]; Select[ Prime@ Range@ 20000, spl[#] == 3 &] (* Giovanni Resta, Mar 03 2014 *)

Extensions

Example clarified by Harvey P. Dale, Jun 09 2025

A238500 Primes which are the concatenation of two primes in exactly four ways.

Original entry on oeis.org

233347, 233911, 239929, 337397, 373613, 379397, 733331, 796337, 1321997, 1933331, 2333347, 2333533, 2339929, 2392333, 2393257, 2393761, 2939971, 3136373, 3165713, 3217337, 3319733, 3499277, 3539311, 3727397, 3733967, 3739103, 3739199, 3739397, 3739433
Offset: 1

Views

Author

Colin Barker, Feb 27 2014

Keywords

Examples

			233347 is in the sequence because 2, 33347, 23, 3347, 233, 347, 2333 and 47 are all primes, so there are four ways.

Links

Crossrefs

Cf. A105184, A238056, A238057, A238499.

Programs

  • Mathematica
    spl[n_] := Block[{d = IntegerDigits@n, c = 0, z}, z = Length@d; Do[If[PrimeQ@ FromDigits@ Take[d, k] && d[[k + 1]] > 0 && PrimeQ@ FromDigits@ Take[d, k - z], c++], {k, z - 1}]; c]; Select[ Prime@ Range@ 250000, spl[#] == 4 &] (* Giovanni Resta, Mar 03 2014 *)

A238647 Primes which are not the concatenation of two primes.

Original entry on oeis.org

2, 3, 5, 7, 11, 13, 17, 19, 29, 31, 41, 43, 47, 59, 61, 67, 71, 79, 83, 89, 97, 101, 103, 107, 109, 127, 131, 139, 149, 151, 157, 163, 167, 179, 181, 191, 199, 227, 239, 251, 257, 263, 269, 277, 281, 307, 349, 401, 409, 419, 421, 431, 439, 443, 449, 457, 461
Offset: 1

Views

Author

Colin Barker, Mar 02 2014

Keywords

Comments

223 is the first term in A141409 which is not in this sequence.
In this sequence, a prime preceded by one or more zeros is not considered to be a prime.

Examples

			59 is in the sequence because 5 is prime but 9 is not prime.
223 is not in the sequence because both 2 and 23 are primes.

Crossrefs

Cf. A141409, A105184 (complement), A238056, A238057, A238499.
Showing 1-5 of 5 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.