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.

A238056 Primes which are the concatenation of two primes 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, 311, 331, 337, 347, 353, 359, 367, 379, 383, 389, 397, 433, 523, 541, 547, 571, 593, 613, 617, 673, 677, 719, 733, 743, 761, 773, 977, 1013, 1033, 1093, 1097, 1117, 1123, 1129
Offset: 1

Views

Author

Colin Barker, Feb 17 2014

Keywords

Comments

This is not a duplicate of A129800, which accepts "07" for example as the second prime.

Examples

			113 is in the sequence because 11 and 3 are both primes, but 1 and 13 are not both primes, so there is one way.

Links

Crossrefs

Cf. A105184, A238057, A129800.
Cf. A010051, A000040.

Programs

  • Haskell
    a238056 n = a238056_list !! (n-1)
a238056_list = filter ((== 1) . 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@ 300, spl[#] == 1 &] (* Giovanni Resta, Feb 27 2014 *)

A383811 Primes which satisfy the requirements of A380943 in exactly two ways.

Original entry on oeis.org

373, 1913, 3733, 6737, 7937, 11353, 13997, 19997, 23773, 24113, 29347, 31181, 31193, 31907, 34729, 37277, 38237, 41593, 47293, 59929, 71971, 72719, 73823, 74177, 79337, 79613, 82373, 83773, 83911, 88397, 100913, 111773, 111973, 118171, 118273, 118747, 132113, 132137, 139547
Offset: 1

Views

Author

James C. McMahon and Robert G. Wilson v, May 17 2025

Keywords

Comments

The requirements of A380943 are that primes, p_n, written in decimal representation by the concatenation of primes p and q such that the concatenation of q and p also forms a prime.

Examples

			373 is a member since 373 is the 74th prime, p=3 and q=73, and the reverse concatenation is 733 which is the 130th prime. In another way, p=37 and q=3, and the reverse concatenation is 337, the 68th prime.

Crossrefs

Cf. A000040, A238057, A380943, A383810, A383812, A383813, A383814, A383815, A383816.

Programs

  • Mathematica
    f[n_] := Block[{cnt = 0, id = IntegerDigits@ n, k = 1, len, p, q, qp}, len = Length@ id; While[k < len, p = Take[id, k]; q = Take[id, -len + k]; qp = FromDigits[ Join[q, p]]; If[ PrimeQ[FromDigits[p]] && PrimeQ[FromDigits[q]] && PrimeQ[qp] && IntegerLength[qp] == len, cnt++]; k++]; cnt];Select[ Prime@ Range@ 13000, f@# == 2 &]

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.

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