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.

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A383813 Primes which satisfy the requirements of A380943 in exactly four ways.

Original entry on oeis.org

257931013, 1394821313, 2699357347, 3122419127, 3132143093, 3647381953, 3736320359, 3799933727, 6130099337, 7622281937, 7943701397, 7991407367
Offset: 1

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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, 0, 0, 0, 1, 12, ..., .

Crossrefs

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@ 10000000, f@# == 4 &]

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

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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.
		

Crossrefs

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
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