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 1-5 of 5 results.

A257498 Numbers n such that the decimal expansions of both n and n^2 have 3 as the digit with the smallest value and 8 as the digit with the largest value.

Original entry on oeis.org

7378, 66834, 67438, 67738, 73874, 86356, 577378, 577438, 586374, 658388, 666834, 667438, 676438, 683874, 683876, 684438, 688374, 738474, 738538, 743878, 744538, 744738, 747378, 747438, 763844, 764438, 765738, 766384, 863388, 863474, 873874, 874378, 875434
Offset: 1

Views

Author

Felix Fröhlich, Apr 27 2015

Keywords

Links

Crossrefs

Cf. A256630, A256631, A256633, A256634, A256708, A256709, A256889, A257197, A257210, A257211, A256601, A257310, A249915, A257123, A257368, A257485, A257486, A238553, A257534.

Programs

  • Mathematica
    fQ[n_] := Block[{c = DigitCount@ n}, And[Plus @@ Take[c, {1, 2}] == 0, Plus @@ Take[c, {9, 10}] == 0, c[[3]] > 0, c[[8]] > 0]]; Select[Range@ 1000000, fQ@ # && fQ[#^2] &] (* Michael De Vlieger, May 05 2015 *)
  • PARI
    is(n) = vecmin(digits(n))==3 && vecmin(digits(n^2))==3 && vecmax(digits(n))==8 && vecmax(digits(n^2))==8

A254071 Numbers n such that the decimal expansions of both n and n^2 have 4 as the digit with the smallest value and 8 as the digit with the largest value.

Original entry on oeis.org

684, 6684, 8874, 66684, 68474, 74758, 76478, 86478, 666684, 668474, 675684, 744758, 766458, 6666684, 6668474, 6675684, 6748678, 6845784, 7586478, 8686574, 8875684, 66666684, 66756684, 74744758, 74758576, 75858874, 75867574, 76464878, 86878458, 87546878
Offset: 1

Views

Author

Felix Fröhlich, May 03 2015

Keywords

Links

Crossrefs

Cf. A256630, A256631, A256633, A256634, A256708, A256709, A256889, A257197, A257210, A257211, A256601, A257310, A249915, A257123, A257368, A257485, A257486, A257498, A238553.

Programs

  • Mathematica
    fQ[n_] := Block[{c = DigitCount@ n}, And[Plus @@ Take[c, {1, 3}] == 0, Plus @@ Take[c, {9, 10}] == 0, c[[4]] > 0, c[[8]] > 0]]; Select[Range@ 1000000, fQ@ # && fQ[#^2] &] (* Michael De Vlieger, May 05 2015 *)
  • PARI
    is(n) = vecmin(digits(n))==4 && vecmin(digits(n^2))==4 && vecmax(digits(n))==8 && vecmax(digits(n^2))==8

A257534 Numbers n such that the decimal expansions of both n and n^2 have 4 as the digit with the smallest value and 7 as the digit with the largest value.

Original entry on oeis.org

74, 74476, 74474476
Offset: 1

Views

Author

Felix Fröhlich, Apr 28 2015

Keywords

Comments

Subsequence of A136948 and of A137139.
a(4) > 10^19, if it exists. - Giovanni Resta, May 11 2015
From Jon E. Schoenfield, Jun 28 2015: (Start)
a(4) > 6.6666...*10^28, if it exists.
Define a property P1 such that, for any positive integer k, P1(k) is true iff the smallest- and largest-valued digits of the decimal expansion of k are 4 and 7, respectively. This sequence lists the positive integers n such that both P1(n) and P1(n^2) are true.
Define a less-restrictive property P2 such that, for any positive integer k, P2(k) is true iff the smallest- and largest-valued digits of the decimal expansion of k are at least 4 and at most 7, respectively. There exist only four positive integers n < 6.6666...*10^28, such that both P2(n) and P2(n^2) are true: a(1), a(2), a(3), and 76 (whose square, 5776, has minimum digit 5).
Conjecture: a(4) does not exist. (End)
a(4) > 7.44*10^36, if it exists. - Chai Wah Wu, Sep 09 2017

Crossrefs

Cf. A136948, A137139.
Cf. A256630, A256631, A256633, A256634, A256708, A256709, A256889, A257197, A257210, A257211, A256601, A257310, A249915, A257123, A257368, A257485, A257486, A257498, A238553, A254071, A254072, A254074.

Programs

  • Mathematica
    fQ[n_] := Block[{c = DigitCount@ n}, And[Plus @@ Take[c, {1, 3}] == 0, Plus @@ Take[c, {8, 10}] == 0, c[[4]] > 0, c[[7]] > 0]]; Select[Range@ 1000000, fQ@ # && fQ[#^2] &] (* Michael De Vlieger, May 05 2015 *)
  • PARI
    is(n) = vecmin(digits(n))==4 && vecmin(digits(n^2))==4 && vecmax(digits(n))==7 && vecmax(digits(n^2))==7

A254072 Numbers n such that the decimal expansions of both n and n^2 have 4 as the digit with the smallest value and 9 as the digit with the largest value.

Original entry on oeis.org

974, 9476, 9874, 69684, 94588, 94657, 94788, 94867, 97457, 99476, 99784, 669684, 677974, 697764, 699684, 699764, 699784, 746957, 869457, 945857, 946878, 946888, 947457, 947574, 947886, 947887, 947976, 948678, 974457, 974474, 984878, 998784, 6669684, 6696684
Offset: 1

Views

Author

Felix Fröhlich, May 03 2015

Keywords

Links

Crossrefs

Cf. A256630, A256631, A256633, A256634, A256708, A256709, A256889, A257197, A257210, A257211, A256601, A257310, A249915, A257123, A257368, A257485, A257486, A257498, A238553, A257534, A254071.

Programs

  • Mathematica
    fQ[n_] := Block[{c = DigitCount@ n}, And[Plus @@ Take[c, {1, 3}] == 0, Last@ c == 0, c[[4]] > 0, c[[9]] > 0]]; Select[Range@ 1000000, fQ@ # && fQ[#^2] &] (* Michael De Vlieger, May 05 2015 *)
  • PARI
    is(n) = vecmin(digits(n))==4 && vecmin(digits(n^2))==4 && vecmax(digits(n))==9 && vecmax(digits(n^2))==9

A254074 Numbers k such that the decimal expansions of both k and k^2 have 5 as the digit with the smallest value and 9 as the digit with the largest value.

Original entry on oeis.org

759576, 97759786, 97957576, 887579686, 987759576, 987859786, 7599859786, 7679576587, 8756697886, 8766958976, 9775989867, 9897756766, 9978965766, 76797588887, 88766997576, 97978858887, 99777685676, 99789658666, 99879856766, 767897685676, 869866586666
Offset: 1

Views

Author

Felix Fröhlich, May 03 2015

Keywords

Comments

The first digit of a term is either 7, 8 or 9 and the last digit is either 5, 6 or 7. Conjecture: no term is a multiple of 5. - Chai Wah Wu, Sep 10 2017

Links

Crossrefs

Cf. A137147, A256630, A256631, A256633, A256634, A256708, A256709, A256889, A257197, A257210, A257211, A256601, A257310, A249915, A257123, A257368, A257485, A257486, A257498, A238553, A257534, A254071.

Programs

  • Mathematica
    fQ[n_] := Block[{c = DigitCount@ n}, And[Plus @@ Take[c, {1, 4}] == 0, Last@ c == 0, c[[5]] > 0, c[[9]] > 0]]; Select[Range@ 10000000, fQ@ # && fQ[#^2] &] (* Michael De Vlieger, May 05 2015 *)
  • PARI
    is(n) = vecmin(digits(n))==5 && vecmin(digits(n^2))==5 && vecmax(digits(n))==9 && vecmax(digits(n^2))==9

Extensions

a(14)-a(21) from Hiroaki Yamanouchi, May 07 2015
Showing 1-5 of 5 results.

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