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 1-7 of 7 results.

A338839 No odd digit is present in a(n) + a(n+1).

Original entry on oeis.org

0, 2, 4, 16, 6, 14, 8, 12, 10, 18, 22, 20, 24, 36, 26, 34, 28, 32, 30, 38, 42, 40, 44, 156, 46, 154, 48, 152, 50, 150, 52, 148, 54, 146, 56, 144, 58, 142, 60, 140, 62, 138, 64, 136, 66, 134, 68, 132, 70, 130, 72, 128, 74, 126, 76, 124, 78, 122, 80, 120, 82, 118, 84, 116, 86, 114, 88, 112, 90, 110, 92
Offset: 1

Views

Author

Eric Angelini and Carole Dubois, Nov 11 2020

Keywords

Comments

This is the lexicographically earliest sequence of distinct nonnegative terms with this property.

Examples

			a(1) + a(2) = 0 + 2 = 2 (no odd digit is present);
a(2) + a(3) = 2 + 4 = 6 (no odd digit is present);
a(3) + a(4) = 4 + 16 = 20 (no odd digit is present); etc.

Links

Crossrefs

Cf. A014263 (no odd digit).
Cf. A338840, A338841, A338842, A338843, A338844, A338845, A338846 (variants on the same idea).

Programs

  • Mathematica
    Block[{a = {0}}, Do[Block[{k = 2}, While[Nand[FreeQ[a, k], AllTrue[IntegerDigits@ Total[a[[-1]] + k], EvenQ]], k += 2]; AppendTo[a, k]], {i, 2, 71}]; a] (* Michael De Vlieger, Nov 12 2020 *)

A338841 No odd digit is present in a(n) * a(n+1).

Original entry on oeis.org

0, 1, 2, 3, 8, 5, 4, 6, 7, 12, 17, 24, 10, 20, 11, 22, 13, 16, 14, 19, 32, 9, 52, 39, 58, 36, 18, 26, 31, 28, 15, 40, 21, 42, 53, 54, 46, 44, 47, 60, 34, 59, 38, 69, 94, 30, 68, 33, 62, 43, 48, 50, 56, 73, 88, 23, 96, 25, 80, 35, 64, 41, 104, 27, 84, 51, 122, 71, 66, 37, 72, 29, 76, 79, 112, 74, 63, 102, 61
Offset: 1

Views

Author

Eric Angelini and Carole Dubois, Nov 11 2020

Keywords

Comments

This is the lexicographically earliest sequence of distinct nonnegative terms with this property and also a permutation of the nonnegative integers.

Examples

			a(1) * a(2) = 0 * 1 = 0 (no odd digit is present);
a(2) * a(3) = 1 * 2 = 2 (no odd digit is present);
a(3) * a(4) = 2 * 3 = 6 (no odd digit is present);
a(4) * a(5) = 3 * 8 = 24 (no odd digit is present); etc.

Links

Crossrefs

Cf. A014263 (no odd digits).
Cf. A338839, A338840, A338842, A338843, A338844, A338845, A338846 (variants on the same idea).

Programs

  • Mathematica
    Block[{a = {0}}, Do[Block[{k = 1}, While[Nand[FreeQ[a, k], NoneTrue[IntegerDigits@ Total[a[[-1]]*k], OddQ]], k++]; AppendTo[a, k]], {i, 2, 79}]; a] (* Michael De Vlieger, Nov 12 2020 *)

A338842 No even digit is present in a(n) * a(n+1).

Original entry on oeis.org

1, 3, 5, 7, 11, 9, 13, 15, 21, 17, 23, 25, 31, 43, 37, 27, 19, 29, 33, 35, 45, 39, 41, 77, 49, 73, 81, 71, 47, 79, 65, 51, 61, 55, 57, 63, 53, 67, 59, 87, 85, 91, 83, 93, 101, 75, 69, 113, 141, 95, 105, 127, 119, 129, 133, 135, 117, 147, 213, 149, 115, 97, 103, 151, 209, 153, 235, 169, 233, 143, 137, 229
Offset: 1

Views

Author

Eric Angelini and Carole Dubois, Nov 11 2020

Keywords

Comments

This is the lexicographically earliest sequence of distinct positive terms with this property.

Examples

			a(1) * a(2) = 1 * 3 = 3 (no even digit is present);
a(2) * a(3) = 3 * 5 = 15 (no even digit is present);
a(3) * a(4) = 5 * 7 = 35 (no even digit is present); etc.

Links

Crossrefs

Cf. A014261 (no even digits).
Cf. A338839, A338840, A338841, A338843, A338844, A338845, A338846 (variants on the same idea).

Programs

  • Mathematica
    Block[{a = {1}}, Do[Block[{k = 3}, While[Nand[FreeQ[a, k], NoneTrue[IntegerDigits@ Total[a[[-1]]*k], EvenQ]], k += 2]; AppendTo[a, k]], {i, 2, 72}]; a] (* Michael De Vlieger, Nov 12 2020 *)

A338843 No prime digit is present in a(n) + a(n+1).

Original entry on oeis.org

0, 1, 3, 5, 4, 2, 6, 8, 10, 9, 7, 11, 29, 12, 28, 13, 27, 14, 26, 15, 25, 16, 24, 17, 23, 18, 22, 19, 21, 20, 40, 41, 39, 30, 31, 33, 35, 34, 32, 36, 44, 37, 43, 38, 42, 46, 45, 49, 47, 51, 48, 50, 54, 52, 56, 53, 55, 59, 57, 61, 58, 60, 80, 64, 76, 65, 75, 66, 74, 67, 73, 68, 72, 69, 71, 70, 78, 62
Offset: 1

Views

Author

Eric Angelini and Carole Dubois, Nov 11 2020

Keywords

Comments

The prime digits are 2, 3, 5 and 7. This is the lexicographically earliest sequence of distinct nonnegative terms with this property and also a permutation of the nonnegative integers.

Examples

			a(1) + a(2) = 0 + 1 = 1 (no prime digit is present);
a(2) + a(3) = 1 + 3 = 4 (no prime digit is present);
a(3) + a(4) = 3 + 5 = 8 (no prime digit is present); etc.

Links

Crossrefs

Cf. A202268 (no prime digits).
Cf. A338839, A338840, A338841, A338842, A338844, A338845, A338846 (variants on the same idea).

Programs

  • Mathematica
    Block[{a = {0}}, Do[Block[{k = 1}, While[Nand[FreeQ[a, k], NoneTrue[IntegerDigits@ Total[a[[-1]] + k], PrimeQ]], k++]; AppendTo[a, k]], {i, 2, 78}]; a] (* Michael De Vlieger, Nov 12 2020 *)

A338844 No prime digits are present in a(n) * a(n+1).

Original entry on oeis.org

0, 1, 4, 2, 3, 6, 8, 5, 12, 7, 13, 32, 14, 10, 9, 11, 18, 23, 20, 22, 19, 26, 16, 25, 24, 17, 38, 28, 30, 27, 33, 36, 29, 21, 39, 49, 34, 35, 40, 15, 44, 41, 46, 88, 50, 80, 51, 91, 54, 37, 53, 77, 52, 79, 59, 71, 58, 70, 63, 78, 57, 72, 62, 97, 67, 73, 56, 74, 60, 31, 48, 85, 76, 55, 112, 43, 42, 45
Offset: 1

Views

Author

Eric Angelini and Carole Dubois, Nov 11 2020

Keywords

Comments

The prime digits are 2, 3, 5 and 7. This is the lexicographically earliest sequence of distinct nonnegative terms with this property and also a permutation of the nonnegative integers.

Examples

			a(1) * a(2) = 0 * 1 = 0 (no prime digit is present);
a(2) * a(3) = 1 * 4 = 4 (no prime digit is present);
a(3) * a(4) = 4 * 2 = 8 (no prime digit is present);
a(4) * a(5) = 2 * 3 = 6 (no prime digit is present);
a(5) * a(6) = 3 * 6 = 18 (no prime digit is present); etc.

Links

Crossrefs

Cf. A202268 (no prime digits).
Cf. A338839, A338840, A338841, A338842, A338843, A338845, A338846 (variants on the same idea).

Programs

  • Mathematica
    Block[{a = {0}}, Do[Block[{k = 1}, While[Nand[FreeQ[a, k], NoneTrue[IntegerDigits@ Total[a[[-1]]*k], PrimeQ]], k++]; AppendTo[a, k]], {i, 2, 78}]; a] (* Michael De Vlieger, Nov 12 2020 *)

A338845 No nonprime digit is present in a(n) * a(n+1).

Original entry on oeis.org

1, 2, 11, 3, 9, 8, 4, 13, 21, 12, 6, 37, 15, 5, 7, 36, 62, 86, 27, 101, 22, 16, 17, 19, 28, 84, 33, 69, 83, 31, 25, 23, 14, 18, 29, 77, 49, 48, 74, 78, 94, 38, 194, 378, 199, 127, 175, 43, 54, 143, 39, 57, 41, 55, 61, 53, 44, 58, 134, 248, 224, 123, 45, 75, 47, 59, 97, 26, 202, 161, 157, 46, 82, 271, 87, 256
Offset: 1

Views

Author

Eric Angelini and Carole Dubois, Nov 11 2020

Keywords

Comments

The nonprime digits are 0, 1, 4, 6, 8 and 9. This is the lexicographically earliest sequence of distinct positive terms with this property.

Examples

			a(1) * a(2) = 1 * 2 = 2 (no nonprime digit is present);
a(2) * a(3) = 2 * 11 = 22 (no nonprime digit is present);
a(3) * a(4) = 11 * 3 = 33 (no nonprime digit is present);
a(4) * a(5) = 3 * 9 = 27 (no nonprime digit is present); etc.

Links

Crossrefs

Cf. A338839, A338840, A338841, A338842, A338843, A338844, A338846 (variants on the same idea).

Programs

  • Maple
    N:= 500: # for terms before the first term >= N
S:= select(t -> t mod 10 <> 0, [$2...N]):
nS:= nops(S):
V:=Vector(N):
V[1]:= 1:
for n from 2 do
  for i from 1 to nS+2-n do
    s:= S[i];
    if convert(convert(V[n-1]*s,base,10),set) subset {2,3,5,7} then
      V[n]:= s;
      S:= subsop(i=NULL,S);
      break
    fi;
  od;
  if V[n] = 0 then break fi;
od:
convert(V[1..n-1],list); # Robert Israel, Nov 18 2020
  • Mathematica
    Block[{a = {1}}, Do[Block[{k = 1}, While[Nand[FreeQ[a, k], NoneTrue[IntegerDigits@ Total[a[[-1]]*k], ! PrimeQ@ # &]], k++]; AppendTo[a, k]], {i, 2, 76}]; a] (* Michael De Vlieger, Nov 12 2020 *)

A338846 No nonprime digit is present in a(n) + a(n+1).

Original entry on oeis.org

0, 2, 1, 4, 3, 19, 6, 16, 7, 15, 8, 14, 9, 13, 10, 12, 11, 21, 31, 22, 5, 17, 18, 34, 23, 29, 24, 28, 25, 27, 26, 46, 176, 47, 30, 42, 33, 20, 32, 40, 35, 37, 36, 39, 38, 184, 41, 181, 44, 178, 45, 177, 48, 174, 49, 173, 50, 172, 51, 171, 52, 170, 53, 169, 54, 168, 55, 167, 56, 166, 57, 165, 58, 164, 59
Offset: 1

Views

Author

Eric Angelini and Carole Dubois, Nov 11 2020

Keywords

Comments

The nonprime digits are 0, 1, 4, 6, 8 and 9. This is the lexicographically earliest sequence of distinct nonnegative terms with this property and also a permutation of the nonnegative integers.

Examples

			a(1) + a(2) = 0 + 2 = 2 (no nonprime digit is present);
a(2) + a(3) = 2 + 1 = 3 (no nonprime digit is present);
a(3) + a(4) = 1 + 4 = 5 (no nonprime digit is present);
a(4) + a(5) = 4 + 3 = 7 (no nonprime digit is present);
a(5) + a(6) = 3 + 19 = 22 (no nonprime digit is present); etc.

Links

Crossrefs

Cf. A338839, A338840, A338841, A338842, A338843, A338844, A338845 (variants on the same idea).

Programs

  • Maple
    N:= 1000: # for terms before the first term > N
S:= [$1...N]:
V:=Vector(N):
for n from 2 to N do
  for i from 1 to N+2-n do
    s:= S[i];
    if convert(convert(V[n-1]+s,base,10),set) subset {2,3,5,7} then
      V[n]:= s;
      S:= subsop(i=NULL,S);
      break
    fi;
  od;
  if V[n] = 0 then break fi
od:
convert(V[1..n-1],list); # Robert Israel, Nov 18 2020
  • Mathematica
    Block[{a = {0}}, Do[Block[{k = 1}, While[Nand[FreeQ[a, k], NoneTrue[IntegerDigits@ Total[a[[-1]] + k], ! PrimeQ@ # &]], k++]; AppendTo[a, k]], {i, 2, 75}]; a] (* Michael De Vlieger, Nov 12 2020 *)
Showing 1-7 of 7 results.

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