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.

A083737 Pseudoprimes to bases 2, 3 and 5.

Original entry on oeis.org

1729, 2821, 6601, 8911, 15841, 29341, 41041, 46657, 52633, 63973, 75361, 101101, 115921, 126217, 162401, 172081, 188461, 252601, 294409, 314821, 334153, 340561, 399001, 410041, 488881, 512461, 530881, 552721, 658801, 670033, 721801, 748657
Offset: 1

Views

Author

Serhat Sevki Dincer (sevki(AT)ug.bilkent.edu.tr), May 05 2003

Keywords

Comments

a(n) = n-th positive integer k(>1) such that 2^(k-1) == 1 (mod k), 3^(k-1) == 1 (mod k) and 5^(k-1) == 1 (mod k)
See A153580 for numbers k > 1 such that 2^k-2, 3^k-3 and 5^k-5 are all divisible by k but k is not a Carmichael number (A002997).
Note that a(1)=1729 is the Hardy-Ramanujan number. - Omar E. Pol, Jan 18 2009

Examples

			a(1)=1729 since it is the first number such that 2^(k-1) == 1 (mod k), 3^(k-1) == 1 (mod k) and 5^(k-1) == 1 (mod k).

Links

Crossrefs

Proper subset of A052155. Superset of A230722. Cf. A153580, A002997, A001235, A011541.

Programs

  • Mathematica
    Select[ Range[838200], !PrimeQ[ # ] && PowerMod[2, # - 1, # ] == 1 && PowerMod[3, 1 - 1, # ] == 1 && PowerMod[5, # - 1, # ] == 1 & ]
  • PARI
    is(n)=!isprime(n)&&Mod(2,n)^(n-1)==1&&Mod(3,n)^(n-1)==1&&Mod(5,n)^(n-1)==1 \\ Charles R Greathouse IV, Apr 12 2012

Extensions

Edited by Robert G. Wilson v, May 06 2003
Edited by N. J. A. Sloane, Jan 14 2009

A153515 Terms of A122782 which are not Carmichael numbers A002997.

Original entry on oeis.org

1, 4, 10, 15, 20, 65, 124, 190, 217, 310, 435, 781, 1541, 1891, 3565, 3820, 4123, 4495, 5461, 5611, 5662, 5731, 6735, 7449, 7813, 8029, 8290, 9881, 11041, 11476, 12801, 13021, 13333, 13981, 14981, 15751, 16297, 17767, 20345, 20710, 21361, 22791
Offset: 1

Views

Author

Artur Jasinski, Dec 28 2008

Keywords

Comments

Are there entries in this sequence which are also in A153513 ?
Yes. This subsequence starts 721801, 873181, 4504501, 8646121, 9006401, 9863461, 10403641, 10680265,... (similar to A153580). - R. J. Mathar, Mar 30 2011

Links

Crossrefs

Cf. A002997, A122780, A153508, A153513.

Programs

  • Mathematica
    Select[Range[10^4], !PrimeQ[#] && PowerMod[5, #, # ] == Mod[5, #] && Mod[#, CarmichaelLambda[#]] != 1 &] (* Amiram Eldar, Sep 19 2019 *)

A153581 Pseudoprimes to bases 2,3,5 and 7 which are not Carmichael numbers (A002997).

Original entry on oeis.org

721801, 8646121, 10403641, 22885129, 36307981, 42702661, 46094401, 48064021, 52204237, 79398901, 80918281, 81954133, 114329881, 116151661, 143168581, 170782921, 188985961, 217145881, 220531501, 282707461, 299671921, 303373801, 326695141, 353815801, 361307521
Offset: 1

Views

Author

Ray Chandler & Artur Jasinski, Dec 28 2008

Keywords

Comments

Terms congruent to 5 (mod 6): 468950021, 493108481, 659846021, 5936122901, 8144063621, ... - Robert G. Wilson v, Sep 03 2014
Terms not congruent to 1 (mod 12): 468950021, 493108481, 643767931, 659846021, 773131927, 5779230451, 5936122901, 7294056727, 8144063621, 9671001451, ... - Robert G. Wilson v, Sep 03 2014

Links

Crossrefs

Cf. A002997, A083737, A122780, A153508, A153513, A153514, A153515, A153519, A153580.

Programs

  • Mathematica
    fQ[n_] := ! PrimeQ[n] && PowerMod[2, n - 1, n] == 1 && PowerMod[3, n - 1, n] == 1 && PowerMod[5, n - 1, n] == 1 && PowerMod[7, n - 1, n] == 1 && Mod[n, CarmichaelLambda[n]] != 1; Select[ Range[ 365000000], fQ] (* Ray Chandler, Dec 28 2008; corrected by Robert G. Wilson v, Sep 01 2014 *)

Extensions

Terms a(8) and onward from Robert G. Wilson v, Sep 01 2014
Showing 1-3 of 3 results.

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

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