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 1-4 of 4 results.

A383810 Primes which satisfy the requirements of A380943 in more than one way.

Original entry on oeis.org

373, 1913, 3733, 6737, 7937, 11353, 13997, 19937, 19997, 23773, 24113, 29347, 31181, 31193, 31907, 34729, 37277, 38237, 41593, 47293, 59929, 71971, 72719, 73823, 74177, 79337, 79613, 82373, 83773, 83911, 88397, 100913, 103997
Offset: 1

Views

Author

James C. McMahon and Robert G. Wilson v, May 11 2025

Keywords

Comments

The requirements of A380943 are that primes, 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, 1, 5, 31, 285, 930, 5625, 28137, 205416, ....

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, A380943, A383811, 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@ 10000, f@# > 1 &]

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 &]

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 &]

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

Views

Author

James C. McMahon and Robert G. Wilson v, May 23 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, 0, 0, 0, 1, 12, ..., .

Crossrefs

Cf. A000040, A238500, A380943, A383810, A383811, A383812, 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@ 10000000, f@# == 4 &]
Showing 1-4 of 4 results.

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

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