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.

A090584 Smallest number m >= 0 such that n with m threes appended yields a prime or -1 if no such m exists.

Original entry on oeis.org

1, 0, 0, 1, 0, -1, 0, 1, -1, 1, 0, -1, 0, 2, -1, 1, 0, -1, 0, 3, -1, 1, 0, -1, 8, 1, -1, 1, 0, -1, 0, 4, -1, 2, 1, -1, 0, 1, -1, 483, 0, -1, 0, 1, -1, 1, 0, -1, 2, 1, -1, 1, 0, -1, 3, 1, -1, 6, 0, -1, 0, 5, -1, 1, 1, -1, 0, 1, -1, 5, 0, -1, 0, 1, -1, 3, 1, -1, 0, 4, -1, 1, 0, -1, 1, 1, -1, 1, 0, -1, 2, 3, -1, 2, 1, -1, 0, 1, -1, 3, 0, -1, 0, 2, -1, 1, 0, -1, 0, 1
Offset: 1

Views

Author

Chuck Seggelin, Dec 02 2003

Keywords

Comments

a(n) = 0 if n is already prime. a(n) = -1 for n = any multiple of 3 other than 3 itself. The first 5 record holders in this sequence are 1, 14, 20, 25, 40 with the values 1, 2, 3, 8, 483 respectively. 410 may be the next record holder as no solution has been found for it yet. 410 was tested out to 1250 threes with no prime formed.
From Toshitaka Suzuki, May 19 2024: (Start)
The first 6 record holders in this sequence are 1, 14, 20, 25, 40, 410 with the values 1, 2, 3, 8, 483, 37398 respectively. 817 may be the next record holder as no solution has been found for it yet. 817 was tested out to 300000 threes with no prime formed.
a(n) = -1 when n = 37037*k + 2808, 3666, 4070, 9287, 18799, 21574, 28083, 30558, 33300, 33740, 36663 or 36707, because n followed by any positive number, m say, of 3's is divisible by at least one of the primes {7,11,13,37}. (End)

Examples

			a(25) = 8 because eight 3's must be appended to 25 before a prime is formed (2533333333).
a(6) = -1 because no matter how many 3's are appended to 6, the resulting number is always divisible by 3 and can therefore not be prime. [Similarly for any larger multiple of 3. - _M. F. Hasler_, Jun 06 2024]

Links

Crossrefs

Cf. A372262 (m > 0).
Cf. A083747 (The Wilde Primes, i.e. same operation using ones), A090464 (using sevens), A090465 (using nines).

Programs

  • PARI
    apply( {A090584(n, LIM=500)=n%3 && for(m=0, LIM, ispseudoprime(n) && return(m); n=n*10+3); -(n>3)}, [1..55]) \\ Retun value -1 means that a(n) = -1 or, for non-multiples of 3, a(n) > LIM, the search limit given as 2nd (optional) parameter. - M. F. Hasler, Jun 05 2024

Extensions

Name edited by M. F. Hasler, Jun 06 2024

A090465 Smallest number m such that (n+1)*10^m-1 (i.e., n with m nines appended) yields a prime, or -1 if this will always yield a composite number.

Original entry on oeis.org

1, 0, 0, 2, 0, -1, 0, 1, -1, 1, 0, -1, 0, 1, -1, 2, 0, -1, 0, 2, -1, 1, 0, -1, 3, 1, -1, 4, 0, -1, 0, 2, -1, 1, 1, -1, 0, 1, -1, 1, 0, -1, 0, 1, -1, 16, 0, -1, 1, 1, -1, 3, 0, -1, 5, 1, -1, 15, 0, -1, 0, 2, -1, 12, 1, -1, 0, 2, -1, 1, 0, -1, 0, 2, -1, 1, 3, -1, 0, 1, -1, 1, 0, -1, 1, 2, -1, 33, 0, -1, 1, 1, -1, 3, 10, -1, 0, 3, -1, 1, 0, -1, 0, 1, -1, 1, 0, -1
Offset: 1

Views

Author

Chuck Seggelin, Dec 02 2003

Keywords

Comments

The first 9 record holders in this sequence are 1, 4, 25, 28, 46, 88, 374, 416, 466 with the values 1, 2, 3, 4, 16, 33, 57, 70, 203 respectively.
The next 3 record holders are 1342, 1802, 1934 with the values 29711, 45882, 51836 respectively. 4420 may be the next record holder as no solution has been found for it yet. 4420 was tested out to 300000 nines with no prime formed. - Toshitaka Suzuki, May 27 2024

Examples

			a(25) = 3 because three 9's must be appended to 25 before a prime is formed (25999).
a(6) = -1 because no matter how many 9's are appended to 6, the resulting number is always divisible by 3 and can therefore not be prime.

Links

Crossrefs

Cf. A083747 (The Wilde Primes, i.e. same operation using ones), A090584 (using threes), A090464 (using sevens).

Programs

  • Maple
    f:= proc(n) local x,m;
  if n mod 3 = 0 and n <> 3 then return -1 fi;
  x:= n;
  for m from 0 to 10^4 do
   if isprime(x) then return m fi;
    x:= 10*x+9
  od;
fail
end proc:
map(f, [$1..200]); # Robert Israel, Jun 05 2024
  • PARI
    apply( {A090465(n, LIM=500)=n%3 && for(m=0, LIM, ispseudoprime(n) && return(m); n=n*10+9); -(n>3)}, [1..55]) \\ Retun value -1 means that a(n) = -1 or, if n%3 > 0, then possibly a(n) > LIM, the search limit given as second (optional) parameter. - M. F. Hasler, Jun 05 2024

Formula

a(p) = 0 for p prime.
a(n) = -1 if n is a proper multiple of 3.

Extensions

Definition edited by M. F. Hasler, Jun 05 2024

A363922 a(n) = smallest number m > 0 such that n followed by m 7's yields a prime, or -1 if no such m exists.

Original entry on oeis.org

1, 2, 1, 1, 2, 1, -1, 2, 1, 1, 3, 1, 1, -1, 1, 1, 2, 2, 1, 6, -1, 1, 2, 2, 1, 2, 1, -1, 48, 1, 1, 5, 1, 1, -1, 1, 10, 2, 1, 12, 2, -1, 3, 3, 1, 1, 3, 1, -1, 2, 8, 7, 3, 1, 1, -1, 1, 1, 9, 1, 1, 2, -1, 1, 2, 5, 1, 3, 2, -1, 2, 1, 66, 2, 1, 3, -1, 1, 1, 3
Offset: 1

Views

Author

Toshitaka Suzuki, Jul 12 2023

Keywords

Comments

a(n) = -1 when n = 7*k because no matter how many 7's are appended to n, the resulting number is always divisible by 7 and therefore cannot be prime.
a(n) = -1 when n = 15873*k + 891, 1261, 2889, 3263, 3300, 7810, 8917, 9812, 12617, 13024, 14615 or 15066, because n followed by any positive number, m say, of 7's is divisible by at least one of the primes {3,11,13,37}.
Similarly,
a(n) = -1 when n = 11111111*k + 964146, 1207525, 2342974, 3567630, 7525789, 8134540, 8591231 or 9641467 by primes {11,73,101,137};
a(n) = -1 when n = 429000429*k + 23928593, 27079312, 36492115, 41207969, 52285750, 80569929, 89920882, 93857078, 133928703, 217208145, 223492302, 236849444, 239285937, 247857232, 259793116, 270793127, 323985244, 332698824, 333570182, 334985255, 346849554, 364921157, 376698868 or 412079697 by primes {3,11,13,101,9901};
a(n) = -1 when n = 1221001221*k + 14569863, 28792885, 145698637, 167698659, 225079510, 235985156, 247079532, 287928857, 331921124, 399492478, 415286113, 421492500, 437286135, 455985376, 489857474, 529929099, 551921344, 635208563, 709857694, 877208805, 896850104, 993570842, 1029793886 or 1138850346 by primes {3,11,37,101,9901};
a(n) = -1 when n = 1443001443*k + 85928655, 167698659, 176928746, 218921011, 233985154, 247079532, 310492389, 326286024, 376857361, 585793442, 655208583, 700699192, 746208674, 780080065, 791570640, 805850013, 843492922, 859286557, 882570731, 896850104, 1027793884, 1219922012, 1234986155 or 1377858362 by primes {3,13,37,101,9901}.
a(4444) > 300000 or a(4444) = -1.

Examples

			a(11)=3 because 117 and 1177 are composite but 11777 is prime.

Links

Crossrefs

Cf. A008589, A069568, A090464, A113076.

Programs

  • PARI
    a(n) = if ((n%7), my(m=1); while (!isprime(eval(concat(Str(n), Str(7*(10^m-1)/9)))), m++); m, -1); \\ Michel Marcus, Jul 17 2023
Showing 1-3 of 3 results.

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