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.

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A036310 Composite numbers whose prime factors contain no digits other than 2 and 3.

Original entry on oeis.org

4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 46, 48, 54, 64, 69, 72, 81, 92, 96, 108, 128, 138, 144, 162, 184, 192, 207, 216, 243, 256, 276, 288, 324, 368, 384, 414, 432, 446, 466, 486, 512, 529, 552, 576, 621, 648, 669, 699, 729, 736, 768, 828, 864, 892, 932, 972
Offset: 1

Views

Author

Patrick De Geest, Dec 15 1998

Keywords

Comments

All terms are a product of at least two terms of A020458. - David A. Corneth, Oct 09 2020

Links

Crossrefs

Cf. A003586, A020458, A036302-A036325.

Programs

  • Mathematica
    dpfQ[n_]:=Module[{d=Union[Flatten[IntegerDigits/@Transpose[ FactorInteger[ n]][[1]]]]},!PrimeQ[n] && (d=={2}||d=={3}||d=={2,3})]; Select[Range[ 1000], dpfQ] (* Harvey P. Dale, Aug 24 2013 *)

Formula

Sum_{n>=1} 1/a(n) = Product_{p in A020458} (p/(p - 1)) - Sum_{p in A020458} 1/p - 1 = 1.2804224166... . - Amiram Eldar, May 18 2022

A036312 Composite numbers whose prime factors contain no digits other than 2 and 7.

Original entry on oeis.org

4, 8, 14, 16, 28, 32, 49, 56, 64, 98, 112, 128, 196, 224, 256, 343, 392, 448, 454, 512, 554, 686, 784, 896, 908, 1024, 1108, 1372, 1454, 1568, 1589, 1792, 1816, 1939, 2048, 2216, 2401, 2744, 2908, 3136, 3178, 3584, 3632, 3878, 4096, 4432, 4802, 5089, 5488
Offset: 1

Views

Author

Patrick De Geest, Dec 15 1998

Keywords

Comments

All terms are a product of at least two terms of A020459. - David A. Corneth, Oct 09 2020

Links

Crossrefs

Cf. A003591, A020459, A036302-A036325.

Programs

  • Maple
    dmax:= 4: # for terms < 2*10^dmax
P:= {2,7}:
L:= {7}:
for d from 1 to dmax-1 do
  L:= map(t -> 2*10^d+t, L) union map(t -> 7*10^d+t, L);
  P:= P union select(isprime,L);
od:
R:= {1}: N:= 2*10^dmax:
for p in P do
  R:= R union map(t -> seq(t*p^j,j=1..floor(log[p](N/t))), R)
od:
sort(convert(R minus P minus {1},list)); # Robert Israel, Aug 04 2020

Formula

Sum_{n>=1} 1/a(n) = Product_{p in A020459} (p/(p - 1)) - Sum_{p in A020459} 1/p - 1 = 0.7041098484... . - Amiram Eldar, May 18 2022

A036313 Composite numbers whose prime factors contain no digits other than 2 and 9.

Original entry on oeis.org

4, 8, 16, 32, 58, 64, 116, 128, 232, 256, 458, 464, 512, 841, 916, 928, 1024, 1682, 1832, 1856, 1858, 2048, 3364, 3664, 3712, 3716, 4096, 5998, 6641, 6728, 7328, 7424, 7432, 8192, 11996, 13282, 13456, 14656, 14848, 14864, 16384, 19858, 23992, 24389
Offset: 1

Views

Author

Patrick De Geest, Dec 15 1998

Keywords

Comments

All terms are a product of at least two terms of A020460. - David A. Corneth, Oct 09 2020

Links

Crossrefs

Cf. A020460, A036302-A036325.

Programs

  • Maple
    S[1]:= [2,9]:
for d from 2 to 5 do S[d]:= map(t -> (10*t+2,10*t+9), S[d-1]) od:
P29:= select(isprime, map(op,[seq(S[i],i=1..5)])):
N:= 10^5:
R:= {1}:
for p in P29 do
  R:= map(t -> seq(t*p^j,j=0..floor(log[p](N/t))), R)
od:
R:= R minus convert(P29,set) minus {1}:
sort(convert(R,list)); # Robert Israel, Jan 17 2020
  • Mathematica
    pf29Q[n_]:=Module[{pfs=Union[Flatten[IntegerDigits/@Transpose[ FactorInteger[ n]][[1]]]]},MatchQ[pfs,{2}]||MatchQ[pfs,{9} ]||MatchQ[pfs,{2,9}]]; nn=25000;Select[Complement[Range[nn],Prime[ Range[ PrimePi[nn]]]],pf29Q] (* Harvey P. Dale, Apr 23 2012 *)

Formula

Sum_{n>=1} 1/a(n) = Product_{p in A020460} (p/(p - 1)) - Sum_{p in A020460} 1/p - 1 = 0.5433646773... . - Amiram Eldar, May 18 2022

A036314 Composite numbers whose prime factors contain no digits other than 3 and 4.

Original entry on oeis.org

9, 27, 81, 129, 243, 387, 729, 1161, 1299, 1329, 1849, 2187, 3483, 3897, 3987, 5547, 6561, 10029, 10299, 10449, 11691, 11961, 16641, 18619, 19049, 19683, 30087, 30897, 31347, 35073, 35883, 49923, 55857, 57147, 59049, 79507, 90261, 92691
Offset: 1

Views

Author

Patrick De Geest, Dec 15 1998

Keywords

Comments

All terms are a product of at least two terms of A020461. - David A. Corneth, Oct 09 2020

Links

Crossrefs

Cf. A020461, A036302-A036325.

Formula

Sum_{n>=1} 1/a(n) = Product_{p in A020461} (p/(p - 1)) - Sum_{p in A020461} 1/p - 1 = 0.1819438988... . - Amiram Eldar, May 22 2022

A036315 Composite numbers whose prime factors contain no digits other than 3 and 5.

Original entry on oeis.org

9, 15, 25, 27, 45, 75, 81, 125, 135, 159, 225, 243, 265, 375, 405, 477, 625, 675, 729, 795, 1059, 1125, 1215, 1325, 1431, 1765, 1875, 2025, 2187, 2385, 2809, 3125, 3177, 3375, 3645, 3975, 4293, 5295, 5625, 6075, 6561, 6625, 7155, 8427, 8825, 9375, 9531
Offset: 1

Views

Author

Patrick De Geest, Dec 15 1998

Keywords

Comments

Products of at least two terms of A020462. - David A. Corneth, Oct 09 2020

Links

Crossrefs

Cf. A003593, A020462, A036302-A036325.

Programs

  • Mathematica
    Select[Range[10000],SubsetQ[{3,5},Union[Flatten[IntegerDigits/@ FactorInteger[ #][[All,1]]]]]&&CompositeQ[#]&] (* Harvey P. Dale, May 30 2021 *)

Formula

Sum_{n>=1} 1/a(n) = Product_{p in A020462} (p/(p - 1)) - Sum_{p in A020462} 1/p - 1 = 0.3620363317... . - Amiram Eldar, May 22 2022

A036316 Composite numbers whose prime factors contain no digits other than 3 and 7.

Original entry on oeis.org

9, 21, 27, 49, 63, 81, 111, 147, 189, 219, 243, 259, 333, 343, 441, 511, 567, 657, 729, 777, 999, 1011, 1029, 1119, 1323, 1369, 1533, 1701, 1813, 1971, 2187, 2199, 2319, 2331, 2359, 2401, 2611, 2701, 2997, 3033, 3087, 3357, 3577, 3969, 4107, 4599, 5103
Offset: 1

Views

Author

Patrick De Geest, Dec 15 1998

Keywords

Comments

All terms are a product of at least two terms of A020463. - David A. Corneth, Oct 09 2020

Links

Crossrefs

Cf. A003594, A020463, A036302-A036325.

Programs

  • Magma
    [n: n in [9..6000] | not IsPrime(n) and forall{f: f in PrimeDivisors(n) | Intseq(f) subset [3,7]}]; // Bruno Berselli, Aug 26 2013
  • Mathematica
    dpfQ[n_]:=Module[{d=Union[Flatten[IntegerDigits/@Transpose[FactorInteger[n]][[1]]]]}, !PrimeQ[n]&&(d == {3}||d == {7}||d == {3, 7})]; Select[Range[6000], dpfQ] (* Vincenzo Librandi, Aug 25 2013 *)

Formula

Sum_{n>=1} 1/a(n) = Product_{p in A020463} (p/(p - 1)) - Sum_{p in A020463} 1/p - 1 = 0.3143000293... . - Amiram Eldar, May 22 2022

A036317 Composite numbers whose prime factors contain no digits other than 3 and 8.

Original entry on oeis.org

9, 27, 81, 243, 249, 729, 747, 1149, 2187, 2241, 2649, 3447, 6561, 6723, 6889, 7947, 10341, 11499, 19683, 20169, 20667, 23841, 31023, 31789, 34497, 59049, 60507, 62001, 71523, 73289, 93069, 95367, 103491, 114999, 116499, 146689, 177147
Offset: 1

Views

Author

Patrick De Geest, Dec 15 1998

Keywords

Comments

All terms are a product of at least two terms of A020464. - David A. Corneth, Oct 09 2020

Links

Crossrefs

Cf. A020464, A036302-A036325.

Formula

Sum_{n>=1} 1/a(n) = Product_{p in A020464} (p/(p - 1)) - Sum_{p in A020464} 1/p - 1 = 0.1750565813... . - Amiram Eldar, May 22 2022

A036318 Composite numbers whose prime factors contain no digits other than 4 and 7.

Original entry on oeis.org

49, 329, 343, 2209, 2303, 2401, 15463, 16121, 16807, 31129, 52339, 103823, 108241, 112847, 117649, 209009, 217903, 313439, 334439, 351419, 366373, 523229, 542129, 542339, 544229, 726761, 757687, 789929, 823543, 1463063, 1525321, 2104519
Offset: 1

Views

Author

Patrick De Geest, Dec 15 1998

Keywords

Comments

All terms are a product of at least two terms of A020465. - David A. Corneth, Oct 09 2020

Links

Crossrefs

Cf. A020465, A036302-A036325.

Programs

  • Mathematica
    pf47Q[n_]:=Module[{u=Union[Flatten[IntegerDigits/@Transpose[ FactorInteger[ n]][[1]]]]},!PrimeQ[n]&&(u=={4}||u=={7}||u=={4,7})];Select[ Range[ 2200000],pf47Q] (* Harvey P. Dale, Jun 05 2013 *)

Formula

Sum_{n>=1} 1/a(n) = Product_{p in A020465} (p/(p - 1)) - Sum_{p in A020465} 1/p - 1 = 0.0279830135... . - Amiram Eldar, May 22 2022

A036320 Composite numbers whose prime factors contain no digits other than 5 and 7.

Original entry on oeis.org

25, 35, 49, 125, 175, 245, 343, 625, 875, 1225, 1715, 2401, 2785, 2885, 3125, 3785, 3899, 4039, 4375, 5299, 6125, 8575, 12005, 13925, 14425, 15625, 16807, 18925, 19495, 20195, 21875, 26495, 27293, 27785, 28273, 30625, 37093, 37885, 38785
Offset: 1

Views

Author

Patrick De Geest, Dec 15 1998

Keywords

Comments

All terms are a product of at least two terms of A020467. - David A. Corneth, Oct 09 2020

Links

Crossrefs

Cf. A003595, A020467, A036302-A036325.

Formula

Sum_{n>=1} 1/a(n) = Product_{p in A020467} (p/(p - 1)) - Sum_{p in A020467} 1/p - 1 = 0.1179595738... . - Amiram Eldar, May 22 2022

A036321 Composite numbers whose prime factors contain no digits other than 5 and 9.

Original entry on oeis.org

25, 125, 295, 625, 1475, 2995, 3125, 3481, 7375, 14975, 15625, 17405, 35341, 36875, 74875, 78125, 87025, 176705, 184375, 205379, 299995, 358801, 374375, 390625, 435125, 479795, 497795, 883525, 921875, 1026895, 1499975, 1794005, 1871875
Offset: 1

Views

Author

Patrick De Geest, Dec 15 1998

Keywords

Comments

All terms are a product of at least two terms of A020468. - David A. Corneth, Oct 09 2020

Links

Crossrefs

Cf. A020468, A036302-A036325.

Programs

  • Mathematica
    Select[Range[1872000],CompositeQ[#]&&SubsetQ[{5,9},Flatten[ IntegerDigits/@ FactorInteger[#][[All,1]]]]&] (* Harvey P. Dale, Sep 17 2019 *)

Formula

Sum_{n>=1} 1/a(n) = Product_{p in A020468} (p/(p - 1)) - Sum_{p in A020468} 1/p - 1 = 0.0550718517... . - Amiram Eldar, May 22 2022
Previous Showing 11-20 of 25 results. Next

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