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 1-10 of 12 results. Next

A133957 Form the list of home primes A037274(c) for c composite, and sort into increasing order.

Original entry on oeis.org

23, 37, 211, 223, 227, 229, 233, 241, 257, 271, 277, 283, 311, 313, 317, 331, 337, 347, 353, 359, 367, 373, 379, 383, 389, 397, 523, 541, 547, 557, 571, 577, 719, 743, 761, 773, 797, 1117, 1123, 1129, 1153, 1171, 1319, 1361, 1367, 1373, 1723, 1741, 1747
Offset: 1

Views

Author

Robert G. Wilson v, Sep 30 2007

Keywords

Comments

The old name was "Home primes the result of composite numbers."
Number of terms < 10^n: 0, 2, 37, 274, 2087, 15472, 123261, ....
Increasing sequence of all prime numbers which are concatenations of at least two primes ordered in nondecreasing order (e.g., 227=2.2.7, 1319=13.19). - Bartlomiej Pawlik, Aug 06 2023

Examples

			The home primes corresponding to the first few composite numbers c are as follows:
   c            A037274(c)
   4            211
   6            23
   8            3331113965338635107
   9            311
   10           773
   12           223
   14           13367
   15           1129
   16           31636373
   18           233
   20           3318308475676071413
   21           37
   ...          ...

Links

Crossrefs

Cf. A037274, A118756, A133959, A133961, A133963, A133965, A133967, A133969, A133971, A133973, A133975, A133977, A133979.

Programs

  • Mathematica
    lst = {}; f[n_] := FromDigits@ Flatten[ IntegerDigits@ Table[ #[[1]], {#[[2]]}] & /@ FactorInteger@n, 2]; h[n_] := NestWhileList[f@# &, n, !PrimeQ@# &, 1, 28]; Do[p = h[n][[ -1]]; If[ PrimeQ@p && p < 10^7 && p != n, Print[{n, p}]; AppendTo[lst, p]], {n, 2, 1000}]; Union@ lst

Extensions

Entry revised by N. J. A. Sloane, Mar 24 2021

A133959 Home primes whose homeliness is greater than 2.

Original entry on oeis.org

211, 223, 311, 337, 373, 379, 389, 547, 571, 773, 1123, 1129, 1153, 1319, 1931, 2237, 2311, 2341, 2347, 2371, 2383, 2389, 2557, 2719, 2797, 2953, 2971, 3137, 3167, 3181, 3191, 3251, 3257, 3313, 3329, 3331, 3347, 3359, 3373, 3389, 3449, 3457, 3461, 3463
Offset: 1

Views

Author

Robert G. Wilson v, Sep 30 2007

Keywords

Comments

Number of terms < 10^n: 0, 0, 10, 91, 658, 5076, 39095, ....

Examples

			{4, 22, 211} -> 211, etc.

Crossrefs

Cf. A037274, A118756, A133957, A133961, A133963, A133965, A133967, A133969, A133971, A133973, A133975, A133977, A133979.

Programs

  • Mathematica
    lst = {}; f[n_] := FromDigits@ Flatten[ IntegerDigits@ Table[ #[[1]], {#[[2]]}] & /@ FactorInteger@n, 2]; h[n_] := NestWhileList[f@# &, n, !PrimeQ@# &, 1, 28]; Do[p = h[n][[ -1]]; If[ PrimeQ@p && p < 10^7 && p != n, Print[{n, p}]; AppendTo[lst, p]], {n, 2, 10^7}];
d = 3 - 2; lsu = {}; Do[ If[ lst[[n]] == lst[[n + d]], AppendTo[ lsu, lst[[n]] ]], {n, 188004 - d - 1}]; Take[ Union@ lsu, 45]

A133961 Home primes whose homeliness is greater than 3.

Original entry on oeis.org

379, 773, 1129, 2347, 2383, 2389, 3137, 3251, 3331, 3359, 3373, 3389, 3593, 3719, 3761, 3767, 3797, 4397, 4759, 7331, 7457, 7523, 7541, 7547, 7823, 7853, 11251, 13367, 13883, 17137, 17317, 19157, 19181, 22367, 22397, 23131, 23167, 23173
Offset: 1

Views

Author

Robert G. Wilson v, Sep 30 2007

Keywords

Comments

Number of terms < 10^n: 0, 0, 2, 26, 221, 1843, 14516, ....

Examples

			(42,74,237,379) -> 379, etc.

Crossrefs

Cf. A037274, A118756, A133957, A133959, A133963, A133965, A133967, A133969, A133971, A133973, A133975, A133977, A133979.

Programs

  • Mathematica
    lst = {}; f[n_] := FromDigits@ Flatten[ IntegerDigits@ Table[ #[[1]], {#[[2]]}] & /@ FactorInteger@n, 2]; h[n_] := NestWhileList[f@# &, n, !PrimeQ@# &, 1, 28]; Do[p = h[n][[ -1]]; If[ PrimeQ@p && p < 10^7 && p != n, Print[{n, p}]; AppendTo[lst, p]], {n, 2, 1000}];
d = 4 - 2; lsu = {}; Do[ If[ lst[[n]] == lst[[n + d]], AppendTo[ lsu, lst[[n]] ]], {n, 188004 - d - 1}]; Take[ Union@ lsu, 40]

A133964 Home primes whose homeliness is 5.

Original entry on oeis.org

773, 1129, 3137, 3251, 3593, 3797, 7541, 7853, 23167, 23557, 23719, 23743, 23773, 23971, 31973, 33191, 33331, 33769, 33863, 37307, 37573, 37691, 37997, 39733, 39929, 47797, 53101, 61613, 67349, 67709, 71129, 71171, 71443, 71719, 73181
Offset: 1

Views

Author

Robert G. Wilson v, Sep 30 2007

Keywords

Comments

Number of terms < 10^n: 0, 0, 1, 8, 44, 417, 3299, ... .

Examples

			Only (10, 25, 55, 511, 773) -> 773, etc.

Crossrefs

Cf. A037274, A118756, A133963, A133956, A133957, A133958, A133960, A133962, A133966, A133968, A133970, A133972, A133974, A133976, A133978.

Programs

  • Mathematica
    lst = {}; f[n_] := FromDigits@ Flatten[ IntegerDigits@ Table[ #[[1]], {#[[2]]}] & /@ FactorInteger@n, 2]; h[n_] := NestWhileList[f@# &, n, !PrimeQ@# &, 1, 28]; Do[p = h[n][[ -1]]; If[ PrimeQ@p && p < 10^7 && p != n, Print[{n, p}]; AppendTo[lst, p]], {n, 2, 1000}];
d = 5 - 2; lsu = {}; Do[ If[ lst[[n]] == lst[[n + d]] && lst[[n - 1]] != lst[[n]] && lst[[n]] != lst[[n + d + 1]], AppendTo[lsu, lst[[n]]]], {n, 188004 - d - 1}]; Take[Union@ lsu, 45]

A133965 Home primes whose homeliness is greater than 5.

Original entry on oeis.org

3389, 3761, 13367, 23251, 23761, 23929, 31193, 31397, 33797, 36389, 37199, 37463, 37547, 37607, 37643, 37717, 37853, 37907, 37951, 37967, 41863, 41887, 41941, 73331, 74759, 74771, 77269, 77711, 77773, 77797, 83383, 112909, 113779, 114773
Offset: 1

Views

Author

Robert G. Wilson v, Sep 30 2007

Keywords

Comments

Number of terms < 10^n: 0, 0, 0, 2, 31, 341, 2695, ....

Examples

			(118, 259, 737, 801, 1167, 3389) -> 3389, etc.

Crossrefs

Cf. A037274, A118756, A133957, A133959, A133961, A133963, A133967, A133969, A133971, A133973, A133975, A133977, A133979.

Programs

  • Mathematica
    lst = {}; f[n_] := FromDigits@ Flatten[ IntegerDigits@ Table[ #[[1]], {#[[2]]}] & /@ FactorInteger@n, 2]; h[n_] := NestWhileList[f@# &, n, !PrimeQ@# &, 1, 28]; Do[p = h[n][[ -1]]; If[ PrimeQ@p && p < 10^7 && p != n, Print[{n, p}]; AppendTo[lst, p]], {n, 2, 1000}];
d = 6 - 2; lsu = {}; Do[ If[ lst[[n]] == lst[[n + d]], AppendTo[ lsu, lst[[n]] ]], {n, 188004 - d - 1}]; Take[ Union@ lsu, 35]

A133967 Home primes whose homeliness is greater than 6.

Original entry on oeis.org

3761, 13367, 23251, 23761, 31397, 33797, 36389, 37643, 37951, 37967, 77711, 77773, 113779, 131777, 132749, 132953, 134129, 178069, 229751, 233347, 233617, 233743, 233881, 233911, 237547, 293863, 311677, 311821, 312619, 313613, 313619, 313739
Offset: 1

Views

Author

Robert G. Wilson v, Sep 30 2007

Keywords

Comments

Number of terms < 10^n: 0, 0, 0, 1, 12, 144, 1273, ....

Crossrefs

Cf. A037274, A118756, A133957, A133959, A133961, A133963, A133965, A133969, A133971, A133973, A133975, A133977, A133979.

Programs

  • Mathematica
    lst = {}; f[n_] := FromDigits@ Flatten[ IntegerDigits@ Table[ #[[1]], {#[[2]]}] & /@ FactorInteger@n, 2]; h[n_] := NestWhileList[f@# &, n, !PrimeQ@# &, 1, 28]; Do[p = h[n][[ -1]]; If[ PrimeQ@p && p < 10^7 && p != n, Print[{n, p}]; AppendTo[lst, p]], {n, 2, 1000}];
d = 7 - 2; lsu = {}; Do[ If[ lst[[n]] == lst[[n + d]], AppendTo[ lsu, lst[[n]] ]], {n, 188004 - d - 1}]; Take[ Union@ lsu, 35]

A133969 Home primes whose homeliness is greater than 7.

Original entry on oeis.org

3761, 13367, 31397, 77773, 132953, 178069, 229751, 233743, 233911, 312619, 313613, 313739, 313829, 317741, 317903, 333857, 333923, 337397, 337457, 337487, 337661, 337853, 337907, 352489, 357727, 359929, 364627, 370451, 373753, 374159
Offset: 1

Views

Author

Robert G. Wilson v, Sep 30 2007

Keywords

Comments

Number of terms < 10^n: 0, 0, 0, 1, 4, 64, 606, ....

Crossrefs

Cf. A037274, A118756, A133957, A133959, A133961, A133963, A133965, A133967, A133971, A133973, A133975, A133977, A133979.

Programs

  • Mathematica
    lst = {}; f[n_] := FromDigits@ Flatten[ IntegerDigits@ Table[ #[[1]], {#[[2]]}] & /@ FactorInteger@n, 2]; h[n_] := NestWhileList[f@# &, n, !PrimeQ@# &, 1, 28]; Do[p = h[n][[ -1]]; If[ PrimeQ@p && p < 10^7 && p != n, Print[{n, p}]; AppendTo[lst, p]], {n, 2, 1000}];
d = 8 - 2; lsu = {}; Do[ If[ lst[[n]] == lst[[n + d]], AppendTo[ lsu, lst[[n]] ]], {n, 188004 - d - 1}]; Take[ Union@ lsu, 31]

A133971 Home primes whose homeliness is greater than 8.

Original entry on oeis.org

77773, 178069, 229751, 312619, 313613, 313739, 317741, 317903, 337457, 337853, 352489, 359929, 364627, 374531, 374587, 375743, 375997, 378997, 379103, 379187, 379397, 379811, 379997, 389971, 719239, 733391, 742283, 747521, 749711, 771941
Offset: 1

Views

Author

Robert G. Wilson v, Sep 30 2007

Keywords

Comments

Number of terms < 10^n: 0, 0, 0, 0, 1, 31, 288, ....

Crossrefs

Cf. A037274, A118756, A133957, A133959, A133961, A133963, A133965, A133967, A133969, A133973, A133975, A133977, A133979.

Programs

  • Mathematica
    lst = {}; f[n_] := FromDigits@ Flatten[ IntegerDigits@ Table[ #[[1]], {#[[2]]}] & /@ FactorInteger@n, 2]; h[n_] := NestWhileList[f@# &, n, !PrimeQ@# &, 1, 28]; Do[p = h[n][[ -1]]; If[ PrimeQ@p && p < 10^7 && p != n, Print[{n, p}]; AppendTo[lst, p]], {n, 2, 1000}];
d = 9 - 2; lsu = {}; Do[ If[ lst[[n]] == lst[[n + d]], AppendTo[ lsu, lst[[n]] ]], {n, 188004 - d - 1}]; Take[ Union@ lsu, 30]

A133973 Home primes whose homeliness is greater than 9.

Original entry on oeis.org

77773, 312619, 359929, 364627, 374531, 378997, 379811, 747521, 749711, 771941, 777643, 1173463, 1355021, 1389281, 1929311, 1991153, 2314723, 2315641, 2333797, 2336263, 2337397, 2337547, 2337607, 2337691, 2339929, 2373823, 2389853
Offset: 1

Views

Author

Robert G. Wilson v, Sep 30 2007

Keywords

Comments

Number of terms < 10^n: 0, 0, 0, 0, 1, 11, 142, ....

Crossrefs

Cf. A037274, A118756, A133957, A133959, A133961, A133963, A133965, A133967, A133969, A133971, A133975, A133977, A133979.

Programs

  • Mathematica
    lst = {}; f[n_] := FromDigits@ Flatten[ IntegerDigits@ Table[ #[[1]], {#[[2]]}] & /@ FactorInteger@n, 2]; h[n_] := NestWhileList[f@# &, n, !PrimeQ@# &, 1, 28]; Do[p = h[n][[ -1]]; If[ PrimeQ@p && p < 10^7 && p != n, Print[{n, p}]; AppendTo[lst, p]], {n, 2, 1000}];
d = 10 - 2; lsu = {}; Do[ If[ lst[[n]] == lst[[n + d]], AppendTo[ lsu, lst[[n]] ]], {n, 188004 - d - 1}]; Take[ Union@ lsu, 30]

A133975 Home primes whose homeliness is greater than 10.

Original entry on oeis.org

378997, 379811, 747521, 777643, 1173463, 2314723, 2315641, 2333797, 2337397, 2337607, 2337691, 3127979, 3127997, 3136607, 3173761, 3182561, 3371237, 3372371, 3373547, 3373907, 3374729, 3376991, 3377999, 3378317, 3379829
Offset: 1

Views

Author

Robert G. Wilson v, Sep 30 2007

Keywords

Comments

Number of terms < 10^n: 0, 0, 0, 0, 0, 4, 60, ....

Crossrefs

Cf. A037274, A118756, A133957, A133959, A133961, A133963, A133965, A133967, A133969, A133971, A133973, A133977, A133979.

Programs

  • Mathematica
    lst = {}; f[n_] := FromDigits@ Flatten[ IntegerDigits@ Table[ #[[1]], {#[[2]]}] & /@ FactorInteger@n, 2]; h[n_] := NestWhileList[f@# &, n, !PrimeQ@# &, 1, 28]; Do[p = h[n][[ -1]]; If[ PrimeQ@p && p < 10^7 && p != n, Print[{n, p}]; AppendTo[lst, p]], {n, 2, 1000}];
d = 11 - 2; lsu = {}; Do[ If[ lst[[n]] == lst[[n + d]], AppendTo[ lsu, lst[[n]] ]], {n, 188004 - d - 1}]; Take[ Union@ lsu, 30]
Showing 1-10 of 12 results. Next

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

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