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 1-8 of 8 results.

A255203 Primes p for which no bases b with 1 < b < p exist such that p is a base b Wieferich prime.

Original entry on oeis.org

2, 3, 5, 7, 13, 17, 19, 23, 31, 41, 47, 53, 61, 67, 73, 83, 89, 101, 107, 139, 149, 157, 167, 173, 179, 193, 227, 239, 251, 271, 277, 311, 317, 337, 383, 389, 409, 431, 443, 457, 467, 479, 491, 503, 541, 569, 587, 593, 613, 643, 677, 683, 691, 709, 719, 733
Offset: 1

Views

Author

Felix Fröhlich, Feb 17 2015

Keywords

Comments

p = prime(n) such that A242830(n) = 0.

Crossrefs

Cf. A255204, A255205, A255206, A255207, A255208, A255209, A255210.

Programs

  • PARI
    forprime(p=1, , b=2; i=0; while(b < p, if(Mod(b, p^2)^(p-1)==1, i++); b++); if(i==0, print1(p, ", ")))

A255204 Primes p for which exactly one base b with 1 < b < p exists such that p is a base b Wieferich prime.

Original entry on oeis.org

29, 37, 43, 59, 79, 97, 103, 109, 113, 137, 151, 181, 191, 197, 199, 223, 233, 241, 257, 263, 281, 283, 293, 307, 373, 379, 397, 401, 419, 421, 433, 439, 449, 461, 499, 521, 523, 547, 557, 563, 577, 601, 617, 619, 641, 659, 661, 701, 727, 739, 743, 761, 769
Offset: 1

Views

Author

Felix Fröhlich, Feb 17 2015

Keywords

Comments

p = prime(n) such that A242830(n) = 1.

Crossrefs

Cf. A255203, A255205, A255206, A255207, A255208, A255209, A255210.

Programs

  • PARI
    forprime(p=1, , b=2; i=0; while(b < p, if(Mod(b, p^2)^(p-1)==1, i++); b++); if(i==1, print1(p, ", ")))

A255205 Primes p for which exactly two bases b with 1 < b < p exist such that p is a base b Wieferich prime.

Original entry on oeis.org

11, 71, 127, 131, 163, 211, 229, 313, 347, 349, 353, 359, 367, 463, 509, 599, 607, 631, 647, 673, 797, 827, 829, 977, 1021, 1061, 1087, 1109, 1123, 1187, 1327, 1381, 1399, 1429, 1453, 1483, 1493, 1499, 1523, 1531, 1549, 1553, 1607, 1613, 1619, 1621, 1657, 1669
Offset: 1

Views

Author

Felix Fröhlich, Feb 17 2015

Keywords

Comments

p = prime(n) such that A242830(n) = 2.

Crossrefs

Cf. A255203, A255204, A255206, A255207, A255208, A255209, A255210.

Programs

  • PARI
    forprime(p=1, , b=2; i=0; while(b < p, if(Mod(b, p^2)^(p-1)==1, i++); b++); if(i==2, print1(p, ", ")))

A255206 Primes p for which exactly three bases b with 1 < b < p exist such that p is a base b Wieferich prime.

Original entry on oeis.org

269, 331, 571, 863, 883, 907, 1097, 1103, 1291, 1579, 1697, 1741, 2179, 2213, 2221, 2281, 2309, 2311, 2551, 2671, 2677, 2693, 2707, 2789, 2791, 3191, 3253, 3571, 3617, 3877, 3931, 4049, 4787, 4813, 4987, 5021, 5153, 5197, 5227, 5347, 5519, 5669, 5689, 5693
Offset: 1

Views

Author

Felix Fröhlich, Feb 17 2015

Keywords

Comments

p = prime(n) such that A242830(n) = 3.

Crossrefs

Cf. A255203, A255204, A255205, A255207, A255208, A255209, A255210.

Programs

  • PARI
    forprime(p=1, , b=2; i=0; while(b < p, if(Mod(b, p^2)^(p-1)==1, i++); b++); if(i==3, print1(p, ", ")))

A255208 Primes p for which exactly five bases b with 1 < b < p exist such that p is a base b Wieferich prime.

Original entry on oeis.org

653, 4909, 7723, 9811, 13691, 15413, 18133, 18223, 21061, 22147, 25679, 29131, 33923, 35353, 36913, 37633, 46021, 57527, 61819, 66107, 71059, 72643, 77867, 79867, 85061, 87509, 89113, 96757, 97213, 98641, 117977, 118163, 120247, 122209, 123653, 126443, 129061
Offset: 1

Views

Author

Felix Fröhlich, Feb 17 2015

Keywords

Comments

p = prime(n) such that A242830(n) = 5.

Crossrefs

Cf. A255203, A255204, A255205, A255206, A255207, A255209, A255210.

Programs

  • PARI
    forprime(p=1, , b=2; i=0; while(b < p, if(Mod(b, p^2)^(p-1)==1, i++); b++); if(i==5, print1(p, ", ")))

A255209 Primes p for which exactly six bases b with 1 < b < p exist such that p is a base b Wieferich prime.

Original entry on oeis.org

5107, 20771, 51427, 52517, 61417, 66161, 116731, 119359, 128657, 140741, 147647, 150559, 199783, 203773, 213949, 229939, 237283, 261761, 286751, 288929, 303089, 339139, 342373, 381853, 384611, 385657, 475897
Offset: 1

Views

Author

Felix Fröhlich, Feb 17 2015

Keywords

Comments

p = prime(n) such that A242830(n) = 6.

Links

Crossrefs

Cf. A255203, A255204, A255205, A255206, A255207, A255208, A255210.

Programs

  • PARI
    forprime(p=1, , b=2; i=0; while(b < p, if(Mod(b, p^2)^(p-1)==1, i++); b++); if(i==6, print1(p, ", ")))

A255210 Primes p for which exactly seven bases b with 1 < b < p exist such that p is a base-b Wieferich prime.

Original entry on oeis.org

103291, 491531, 534851, 804367, 997961, 1026899, 1062427, 1457389, 1550513, 2327629, 2602307, 3093121, 3137257, 3181481, 3412741, 3497381, 3720179, 3814253, 4087301, 4234057, 4891973, 5063087, 5131237, 5194789, 5736611, 6253349, 6903191, 6906469, 6945047
Offset: 1

Views

Author

Felix Fröhlich, Mar 07 2015

Keywords

Comments

p = prime(n) such that A242830(n) = 7.

Links

Crossrefs

Cf. A255203, A255204, A255205, A255206, A255207, A255208, A255209.

Programs

  • PARI
    forprime(p=1, , b=2; i=0; while(b < p, if(Mod(b, p^2)^(p-1)==1, i++); b++); if(i==7, print1(p, ", ")))

A175932 Smallest prime p such that there exist exactly n integers b such that 1 < b < p and b^(p-1) == 1 (mod p^2) or, equivalently, Fermat quotient q_p(b) == 0 (mod p).

Original entry on oeis.org

2, 29, 11, 269, 487, 653, 5107, 103291, 40487, 2544079, 1093, 3511, 1006003
Offset: 0

Views

Author

Max Alekseyev, Oct 24 2010

Keywords

Comments

a(n) is the smallest prime p such that A242830(PrimePi(p)) = n, PrimePi = A000720. - Jianing Song, Jan 27 2019

Examples

			a(5) = 653 since 653 is the smallest prime with exactly five bases b = 84, 120, 197, 287, 410.

Links

Crossrefs

Cf. A001220, A130912, A248865, A242830.
Subset of A134307.
Cf. also A255203, A255204, A255205, A255206, A255207, A255208, A255209, A255210.

Programs

  • PARI
    first_n_entries(n)=v=vector(n); toGo=n; forprime(p=2, , count=sum(b=2, p-1, Mod(b, p^2)^(p-1)==1); if(count<=(n-1)&!v[count+1], v[count+1]=p; toGo--; if(!toGo, return(v)))) \\ Jeppe Stig Nielsen, Jul 31 2015, changed to include a(0) = 2 by Jianing Song, Feb 05 2019

Extensions

a(0) = 2 prepended by Jianing Song, Jan 27 2019
Showing 1-8 of 8 results.

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