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.

A383812 Primes which satisfy the requirements of A380943 in exactly three ways.

Original entry on oeis.org

19937, 103997, 377477, 577937, 738677, 739397, 877937, 2116397, 3110273, 3314513, 3343337, 3634313, 3833359, 5935393, 7147397, 7276337, 7511033, 7699157, 7723337, 11816911, 14713613, 19132213, 19132693, 19998779, 22739317, 23201359, 31189757, 31614377, 31669931, 31687151
Offset: 1

Views

Author

James C. McMahon and Robert G. Wilson v, May 18 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.
The number of terms <= 10^k beginning with k=1: 0, 0, 0, 0, 1, 7, 19, 70, 299, 1872, ..., .

Crossrefs

Cf. A000040, A238499, A380943, A383810, A383811, 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@ 1980000, f@# == 3 &]

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 1-3 of 3 results.

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

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