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.

Previous Showing 11-17 of 17 results.

A064902 Semiprimes p1*p2 such that p2 mod p1 = 4, with p2 > p1.

Original entry on oeis.org

77, 95, 145, 221, 295, 371, 395, 407, 437, 445, 469, 545, 559, 649, 695, 745, 763, 895, 959, 995, 1057, 1133, 1145, 1159, 1195, 1253, 1345, 1351, 1513, 1517, 1679, 1745, 1795, 1841, 1895, 1939, 1945, 2021, 2045, 2095, 2101, 2195, 2245, 2249, 2395, 2429
Offset: 1

Views

Author

Patrick De Geest, Oct 13 2001

Keywords

Links

Crossrefs

Cf. A001358 (p2 mod p1 = 0), A064899-A064911.

Programs

  • PARI
    isok(n) = my(f = factor(n)); (#f~ == 2) && (vecmax(f[,2]) < 2) && ((f[2,1] % f[1,1]) == 4); \\ Michel Marcus, Apr 16 2018
  • Python
    from sympy import factorint
def is_A064902(n):
    f = factorint(n)
    return (sum([f[i] for i in f]) == 2) and (max(f) % min(f) == 4)
def first_A064902(n):
    x = 1
    an = []
    while len(an) < n:
        if is_A064902(x):an.append(x)
        n += 2
    return an # John Cerkan, Apr 14 2018

Extensions

Offset changed by John Cerkan, Apr 12 2018

A064903 Semiprimes p1*p2 such that p2 > p1 and p2 mod p1 = 5.

Original entry on oeis.org

133, 329, 403, 427, 623, 721, 781, 817, 917, 1079, 1211, 1241, 1417, 1507, 1603, 1799, 1819, 1897, 1991, 2077, 2191, 2231, 2681, 2779, 2923, 2959, 2983, 3073, 3107, 3269, 3443, 3563, 3661, 4121, 4151, 4169, 4249, 4411, 4427, 4709, 4739, 4837, 5033
Offset: 1

Views

Author

Patrick De Geest, Oct 13 2001

Keywords

Links

Crossrefs

Cf. A001358 (p2 mod p1 = 0), A064899-A064911.

Programs

  • Mathematica
    sp5Q[n_]:=Module[{f=Transpose[FactorInteger[n]][[1]]},Mod[Last[f], First[ f]] == 5]; Select[Range[5500],PrimeOmega[#]==2&&sp5Q[#]&] (* Harvey P. Dale, Aug 12 2014 *)

Extensions

Name clarified by Sean A. Irvine, Jul 31 2023
Offset changed by Andrew Howroyd, Aug 13 2024

A064904 Semiprimes p1*p2 such that p2 mod p1 = 6, with p2 > p1.

Original entry on oeis.org

91, 187, 247, 287, 391, 581, 667, 671, 679, 913, 923, 973, 1147, 1169, 1261, 1267, 1397, 1561, 1591, 1639, 1757, 1919, 1927, 1937, 2051, 2123, 2149, 2443, 2491, 2641, 2933, 2951, 3031, 3091, 3127, 3227, 3281, 3521, 3817, 3841, 3859, 4087, 4109, 4207
Offset: 1

Views

Author

Patrick De Geest, Oct 13 2001

Keywords

Links

Crossrefs

Cf. A001358 (p2 mod p1 = 0), A064899-A064911.

Programs

  • Mathematica
    Module[{pp=200},Select[Union[Times@@@Select[Subsets[Prime[Range[pp]],{2}],Mod[#[[2]],#[[1]]]==6&]],#<=7Prime[pp]&]](* Harvey P. Dale, Oct 08 2020 *)
  • PARI
    isok(n) = my(f = factor(n)); (#f~ == 2) && (vecmax(f[,2]) < 2) && ((f[2,1] % f[1,1]) == 6); \\ Michel Marcus, Apr 16 2018
  • Python
    from sympy import factorint
def is_A064904(n):
    f = factorint(n)
    return (sum([f[i] for i in f]) == 2) and (max(f) % min(f) == 6) # John Cerkan, Apr 14 2018

Extensions

Offset changed by John Cerkan, Apr 12 2018

A064905 Semiprimes p1*p2 such that p2>p1 and p2 mod p1 = 7.

Original entry on oeis.org

319, 697, 767, 803, 1219, 1529, 1577, 1781, 1853, 2119, 2497, 2981, 3133, 3223, 3587, 3649, 3707, 3743, 3809, 3949, 4061, 4393, 4747, 5161, 5249, 5321, 5401, 5837, 5899, 5909, 5983, 5989, 6127, 6509, 6611, 6631, 6931, 7633, 7697, 8063, 8203, 8473, 8797, 8879
Offset: 1

Views

Author

Patrick De Geest, Oct 13 2001

Keywords

Links

Crossrefs

Cf. A001358 (p2 mod p1 = 0), A064899-A064911.

Programs

  • Mathematica
    m7Q[n_]:=Module[{f=Transpose[FactorInteger[n]][[1]]},Length[f]==2 && Mod[ f[[2]],f[[1]]]==7]; Select[Range[10000], And[m7Q[#], SquareFreeQ[#]] &] (* Harvey P. Dale, May 02 2016; corrected by Michael De Vlieger, Jul 31 2023  *)
nn = 8900; m = 7; Union@ Flatten@ Table[p = Prime[i]; Table[q = Prime[j]; If[Mod[q, p] == m, p q, Nothing], {j, i + 1, PrimePi[nn/p]}], {i, PrimePi[nn]}] (* Michael De Vlieger, Jul 31 2023 *)

Extensions

Corrected and extended by Harvey P. Dale, May 02 2016
Original data restored, name clarified, and offset corrected by Sean A. Irvine, Jul 31 2023

A064906 Semiprimes p1*p2 such that p2 > p1 and p2 mod p1 = 8.

Original entry on oeis.org

209, 451, 611, 713, 949, 1003, 1073, 1177, 1661, 1903, 1957, 1963, 2159, 2629, 2977, 3113, 3131, 3233, 3401, 3653, 3839, 3893, 3953, 3991, 4471, 4667, 5053, 5371, 5533, 5567, 5609, 5627, 5891, 6017, 6019, 6119, 6259, 6289, 6743, 7003, 7033, 7061, 7141
Offset: 1

Views

Author

Patrick De Geest, Oct 13 2001

Keywords

Links

Crossrefs

Cf. A001358 (p2 mod p1 = 0), A064899-A064911.

Programs

  • Mathematica
    spQ[n_]:=Module[{fi=Transpose[FactorInteger[n]],a,b},a=fi[[1]];b= fi[[2]]; Length[a]==2&&Max[b]==1&&Mod[a[[2]],a[[1]]]==8]; Select[Range[ 8000],spQ] (* Harvey P. Dale, Sep 16 2014 *)

Extensions

Offset corrected and name clarified by Sean A. Irvine, Jul 31 2023

A064907 Semiprimes p1*p2 such that p2 mod p1 = 9, with p2 > p1.

Original entry on oeis.org

341, 583, 731, 793, 893, 1067, 1469, 1793, 1807, 1943, 2201, 2323, 2483, 2519, 2761, 3043, 3071, 3487, 3497, 3781, 4213, 4439, 4511, 4777, 4841, 4849, 4939, 5497, 5809, 5933, 5947, 6511, 6539, 6989, 7093, 7117, 7391, 7493, 7601, 7613, 7783, 7891, 7967
Offset: 1

Views

Author

Patrick De Geest, Oct 13 2001

Keywords

Links

Crossrefs

Cf. A001358 (p2 mod p1 = 0), A064899-A064911.

Programs

  • Mathematica
    spQ[n_]:=Module[{fi=FactorInteger[n][[All,1]]},PrimeOmega[n]==2&&Mod[ fi[[2]],fi[[1]]]==9]; Select[Range[8000],spQ]//Quiet (* Harvey P. Dale, Aug 02 2019 *)
  • PARI
    isok(n) = my(f = factor(n)); (#f~ == 2) && (vecmax(f[,2]) < 2) && ((f[2,1] % f[1,1]) == 9); \\ Michel Marcus, Apr 16 2018
  • Python
    from sympy import factorint
def is_A064907(n):
    f = factorint(n)
    return (sum([f[i] for i in f]) == 2) and (max(f) % min(f) == 9)
def list_A064907(cnt):
    inx = 0
    n = 1
    an = []
    while inx < cnt:
        if is_A064907(n):
            an.append(n)
            inx += 1
        n += 2
    return an #John Cerkan, Apr 14 2018

Extensions

Offset changed by John Cerkan, Apr 12 2018

A064908 Semiprimes p1*p2 such that p2 mod p1 = 10, with p2 > p1.

Original entry on oeis.org

299, 473, 551, 1037, 1199, 1271, 1273, 1313, 1441, 1651, 1739, 1817, 2167, 2279, 2327, 2651, 2771, 2813, 2893, 3193, 3341, 3349, 3377, 3439, 3679, 4103, 4331, 4829, 4883, 5071, 5707, 5977, 6049, 6059, 6239, 6281, 6383, 6523, 6817, 7031, 7037, 7097
Offset: 1

Views

Author

Patrick De Geest, Oct 13 2001

Keywords

Links

Crossrefs

Cf. A001358 (p2 mod p1 = 0), A064899-A064911.

Programs

  • PARI
    isok(n) = my(f = factor(n)); (#f~ == 2) && (vecmax(f[,2]) < 2) && ((f[2,1] % f[1,1]) == 10); \\ Michel Marcus, Apr 16 2018
  • Python
    from sympy import factorint
def is_A064908(n):
    f = factorint(n)
    return (sum([f[i] for i in f]) == 2) and (max(f) % min(f) == 10) # John Cerkan, Apr 14 2018

Extensions

Offset changed by John Cerkan, Apr 12 2018
Previous Showing 11-17 of 17 results.

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

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