A113076 -id:A113076 - cp's OEIS frontend

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.

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

Toshitaka Suzuki, Jul 12 2023

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.

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

Toshitaka Suzuki, Table of n, a(n) for n = 1..4443

Cf. A008589, A069568, A090464, A113076.

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

A372056 Smallest prime obtained by appending one or more 3's to n, or -1 if no such prime exists.

Original entry on oeis.org

13, 23, -1, 43, 53, -1, 73, 83, -1, 103, 113, -1, 1333333333333333, 1433, -1, 163, 173, -1, 193, 20333, -1, 223, 233, -1, 2533333333, 263, -1, 283, 293, -1, 313, 323333, -1, 3433, 353, -1, 373, 383, -1

Offset: 1

Toshitaka Suzuki, Mar 30 2024

Next term is 40 followed by 483 3's and is too large to display here (see the b-file).

			For n = 13, a(13) = 1333333333333333 is a prime (but 133,1333,13333 etc. are not primes).

Toshitaka Suzuki, Table of n, a(n) for n = 1..409

See A112394 for another version.

Cf. A030431, A090584, A112386, A113076.

Edited by N. J. A. Sloane, Apr 24 2024

A373859 Smallest prime obtained by appending one or more 9's to n, -1 if no such prime exists.

Original entry on oeis.org

19, 29, -1, 499, 59, -1, 79, 89, -1, 109, 1199999, -1, 139, 149, -1, 1699, 179, -1, 199, 2099, -1, 229, 239, -1, 25999, 269, -1, 289999, 2999, -1, 319999999999999999999999999999, 3299, -1, 349, 359, -1, 379, 389, -1, 409, 419, -1, 439, 449, -1

Offset: 1

Toshitaka Suzuki, Jun 19 2024

Toshitaka Suzuki, Table of n, a(n) for n = 1..448

Cf. A030433, A373201, A112386, A372056, A113076.

from itertools import count
from sympy import isprime
def A373859(n): return next(p for p in ((n+1)*10**m-1 for m in count(1)) if isprime(p)) if n%3 else -1 # Chai Wah Wu, Jul 08 2024

a(11) = 1199999 because 119, 1199, 11999 and 119999 are not primes.

cp's OEIS Frontend

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.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

PARI

A372056 Smallest prime obtained by appending one or more 3's to n, or -1 if no such prime exists.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Extensions

A373859 Smallest prime obtained by appending one or more 9's to n, -1 if no such prime exists.

Views

Author

Keywords

Links

Crossrefs

Programs

Python

Formula