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 1-9 of 9 results.

A065695 Numbers m such that N = (am+1)(bm+1)(cm+1) is a 3-Carmichael number (A087788), where a,b,c = 1,2,53.

Original entry on oeis.org

6120, 11526, 104700, 108516, 115830, 122826, 297726, 298680, 320940, 338430, 339066, 367686, 374046, 387720, 448140, 531456, 534636, 538770, 587106, 618270, 709536, 746106, 762006, 857406, 863766, 897156, 963300, 1115940, 1150920
Offset: 1

Views

Author

Harvey Dubner (harvey(AT)dubner.com), Nov 14 2001

Keywords

Links

Crossrefs

Cf. A064238-A064262, A065696-A065703, A087788.

Programs

  • Mathematica
    CarmichaelNbrQ[n_] := ! PrimeQ@ n && Mod[n, CarmichaelLambda@ n] == 1; Select[ Range@ 1000000, PrimeQ[# + 1] && PrimeQ[2# + 1] && PrimeQ[53# + 1] && CarmichaelNbrQ[(# + 1)(2# + 1)(53# + 1)] &] (* Robert G. Wilson v, Aug 23 2012 *)

Formula

am+1, bm+1, cm+1 are primes and am|(N-1), bm|(N-1), cm|(N-1).

Extensions

More terms from Robert G. Wilson v, Aug 23 2012

A065696 Numbers m such that N = (am+1)(bm+1)(cm+1) is a 3-Carmichael number (A087788), where a,b,c = 1,2,55.

Original entry on oeis.org

3876, 7506, 8166, 16746, 20706, 23676, 24336, 40506, 42156, 68226, 69876, 79776, 95286, 123996, 139176, 149076, 166236, 177786, 183066, 187686, 203856, 210126, 213096, 214086, 216396, 221676, 232566, 265566, 307146, 310116, 321006, 326946
Offset: 1

Views

Author

Harvey Dubner (harvey(AT)dubner.com), Nov 14 2001

Keywords

Links

Crossrefs

Cf. A064238-A064262, A065695, A065696, A065697, A065698, A065699, A065700, A065701, A065703, A087788.

Programs

  • Mathematica
    CarmichaelNbrQ[n_] := ! PrimeQ@ n && Mod[n, CarmichaelLambda@ n] == 1; Select[ Range@ 350000, PrimeQ[# + 1] && PrimeQ[2# + 1] && PrimeQ[55# + 1] && CarmichaelNbrQ[(# + 1)(2# + 1)(55# + 1)] &] (* Robert G. Wilson v, Aug 23 2012 *)

Formula

am+1, bm+1, cm+1 are primes and am|(N-1), bm|(N-1), cm|(N-1).

A065697 Values of m such that N = (am+1)(bm+1)(cm+1) is a 3-Carmichael number (A087788), where a,b,c = 1,2,57.

Original entry on oeis.org

198, 996, 2706, 9090, 13536, 16728, 25620, 33486, 34056, 35310, 41010, 53550, 58566, 60960, 61986, 63240, 72816, 72930, 74526, 75780, 77490, 80340, 83760, 96756, 97326, 100746, 103140, 111918, 125028, 125370, 128676, 129360, 136656, 164700, 174048, 175758, 176898
Offset: 1

Views

Author

Harvey Dubner (harvey(AT)dubner.com), Nov 14 2001

Keywords

Links

Crossrefs

Cf. A064238-A064262, A065695-A065703, A087788.

Programs

  • Mathematica
    CarmichaelNbrQ[n_] := ! PrimeQ@n && Mod[n, CarmichaelLambda@n] == 1; Select[ Range@140000, PrimeQ[# +1] && PrimeQ[2# +1] && PrimeQ[57# +1] && CarmichaelNbrQ[(# +1) (2# +1) (57# +1)] &] (* Robert G. Wilson v, Jul 31 2017 *)

Formula

am+1, bm+1, cm+1 are primes and am|(N-1), bm|(N-1), cm|(N-1).

Extensions

More terms from Amiram Eldar, Oct 17 2019

A065698 Numbers m such that N = (am+1)(bm+1)(cm+1) is a 3-Carmichael number (A087788), where a,b,c = 1,2,61.

Original entry on oeis.org

5580, 19488, 22050, 86466, 140268, 173208, 177966, 227010, 233598, 265806, 273126, 355110, 395736, 402690, 432336, 476988, 486138, 550188, 578370, 588618, 754416, 788088, 844086, 1044288, 1092600, 1204596, 1217406, 1386498, 1415778, 1446888, 1463358, 1563276, 1566936, 1599876
Offset: 1

Views

Author

Harvey Dubner (harvey(AT)dubner.com), Nov 14 2001

Keywords

Links

Crossrefs

Cf. A064238-A064262, A065695-A065703, A087788.

Programs

  • Mathematica
    CarmichaelNbrQ[n_] := ! PrimeQ@n && Mod[n, CarmichaelLambda@ n] == 1; Select[ Range@ 1600000, PrimeQ[# +1] && PrimeQ[2# +1] && PrimeQ[61# +1] &&  CarmichaelNbrQ[(# +1) (2# +1) (61# +1)] &] (* Robert G. Wilson v, Jul 31 2017 *)

Formula

am+1, bm+1, cm+1 are primes and am|(N-1), bm|(N-1), cm|(N-1).

Extensions

a(8) onward from Robert G. Wilson v, Jul 31 2017

A065699 Values of m such that N = (am+1)(bm+1)(cm+1) is a 3-Carmichael number (A087788), where a,b,c = 1,2,63.

Original entry on oeis.org

156, 2550, 3180, 19686, 29640, 40350, 41610, 43626, 46020, 51060, 65550, 72480, 79536, 80670, 85836, 97176, 133716, 150096, 159420, 170760, 184116, 191550, 214986, 229980, 255180, 262110, 278490, 279120, 293106, 294996, 301926, 337080, 350940, 369210, 370596
Offset: 1

Views

Author

Harvey Dubner (harvey(AT)dubner.com), Nov 14 2001

Keywords

Links

Crossrefs

Cf. A064238-A064262, A065695-A065703, A087788.

Programs

  • Mathematica
    carmQ[n_] := CompositeQ[n] && Divisible[n - 1, CarmichaelLambda[n]]; Select[Range[10^5], AllTrue[(v = {1, 2, 63}*# + 1), PrimeQ] && carmQ[Times @@ v] &] (* Amiram Eldar, Oct 17 2019 *)

Formula

am+1, bm+1, cm+1 are primes and am|(N-1), bm|(N-1), cm|(N-1).

Extensions

More terms from Amiram Eldar, Oct 17 2019

A065700 Values of m such that N = (am+1)(bm+1)(cm+1) is a 3-Carmichael number (A087788), where a,b,c = 1,2,65.

Original entry on oeis.org

876, 1656, 7506, 9066, 12966, 33636, 67956, 74586, 83556, 89796, 111636, 126456, 129186, 143616, 150246, 154926, 166626, 184566, 222786, 241116, 252036, 252816, 261786, 271926, 288306, 303906, 304686, 319116, 340956, 344856, 351096, 357726, 362406, 363966, 365526
Offset: 1

Views

Author

Harvey Dubner (harvey(AT)dubner.com), Nov 14 2001

Keywords

Links

Crossrefs

Cf. A064238-A064262, A065695-A065703, A087788.

Programs

  • Mathematica
    carmQ[n_] := CompositeQ[n] && Divisible[n - 1, CarmichaelLambda[n]]; Select[Range[10^5], AllTrue[(v = {1, 2, 65}*# + 1), PrimeQ] && carmQ[Times @@ v] &] (* Amiram Eldar, Oct 17 2019 *)

Formula

am+1, bm+1, cm+1 are primes and am|(N-1), bm|(N-1), cm|(N-1).

Extensions

More terms from Amiram Eldar, Oct 17 2019

A065701 Numbers m such that N = (am+1)(bm+1)(cm+1) is a 3-Carmichael number (A087788), where a,b,c = 1,2,67.

Original entry on oeis.org

11958, 44118, 88740, 97986, 108438, 184416, 245520, 347628, 348030, 418380, 516870, 542598, 546618, 590436, 637470, 674856, 679680, 767316, 809526, 817566, 818370, 888720, 904800, 914046, 930930, 938568, 1006506, 1020978, 1047510, 1070826, 1081278, 1155246, 1209516
Offset: 1

Views

Author

Harvey Dubner (harvey(AT)dubner.com), Nov 14 2001

Keywords

Links

Crossrefs

Cf. A064238-A064262, A065695, A065696, A065697, A065698, A065699, A065700, A065702, A065703, A087788.

Programs

  • Mathematica
    CarmichaelNbrQ[n_] := ! PrimeQ@ n && Mod[n, CarmichaelLambda@ n] == 1; Select[ Range@ 1250000, PrimeQ[# + 1] && PrimeQ[2# + 1] && PrimeQ[67# + 1] && CarmichaelNbrQ[(# + 1)(2# + 1)(67# + 1)] &] (* Robert G. Wilson v, Aug 23 2012 *)

Formula

am+1, bm+1, cm+1 are primes and am|(N-1), bm|(N-1), cm|(N-1).

A065702 Values of m such that N = (am+1)(bm+1)(cm+1) is a 3-Carmichael number (A087788), where a,b,c = 1,2,69.

Original entry on oeis.org

378, 1068, 24390, 29220, 32118, 56130, 70620, 74760, 77658, 82350, 96978, 100980, 110640, 114228, 132858, 152040, 177018, 183090, 186678, 214830, 253608, 282588, 290040, 319158, 342480, 345378, 374358, 388710, 406788, 418380, 428040, 442530, 463230, 463920, 477720
Offset: 1

Views

Author

Harvey Dubner (harvey(AT)dubner.com), Nov 14 2001

Keywords

Links

Crossrefs

Cf. A064238-A064262, A065695-A065703, A087788.

Programs

  • Mathematica
    CarmichaelNbrQ[n_] := ! PrimeQ@ n && Mod[n, CarmichaelLambda@ n] == 1; Select[ Range@ 500000, PrimeQ[# + 1] && PrimeQ[2# + 1] && PrimeQ[69# + 1] && CarmichaelNbrQ[(# + 1)(2# + 1)(69# + 1)] &] (* Robert G. Wilson v, Aug 23 2012 *)

Formula

am+1, bm+1, cm+1 are primes and am|(N-1), bm|(N-1), cm|(N-1).

A101187 Values of m for which (6m+1)(12m+1)(18m+1) is a Carmichael number.

Original entry on oeis.org

1, 5, 6, 11, 15, 22, 33, 35, 45, 51, 55, 56, 61, 85, 96, 100, 103, 105, 115, 121, 195, 206, 216, 225, 242, 255, 276, 370, 380, 426, 455, 470, 506, 510, 511, 550, 561, 588, 609, 628, 661, 700, 710, 741, 800, 805, 825, 871, 920, 930, 975, 1025, 1060, 1115, 1140
Offset: 1

Views

Author

Gerard P. Michon, Dec 03 2004

Keywords

Comments

A046025 is a subsequence giving the values of m for which the three factors are prime, which is a sufficient condition for the product (6m+1)(12m+1)(18m+1) to be a Carmichael number.

Links

Crossrefs

Cf. A002997 (Carmichael numbers), A046025 (subsequence), A101186.
See also A065703.

Programs

  • Magma
    [n: n in [1..1200] | IsOne(t mod CarmichaelLambda(t)) where t is (6*n+1)*(12*n+1)*(18*n+1)]; // Bruno Berselli, Jan 22 2013
  • Mathematica
    CarmichaelNbrQ[n_] := ! PrimeQ@ n && Mod[n, CarmichaelLambda@ n] == 1; Select[ Range@ 1200, CarmichaelNbrQ[(6# + 1)(12# + 1)(18# + 1)] &] (* Robert G. Wilson v, Aug 23 2012 *)
Showing 1-9 of 9 results.

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

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