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 1-4 of 4 results.

A249398 Start with a(1) = 1; then a(n) = smallest number > a(n-1) such that a(n) divides concat(a(n-1),a(n)).

Original entry on oeis.org

1, 2, 4, 5, 10, 20, 25, 50, 100, 125, 200, 250, 400, 500, 625, 1000, 1250, 2000, 2500, 3125, 5000, 6250, 10000, 12500, 15625, 20000, 25000, 31250, 40000, 50000, 62500, 78125, 100000, 125000, 156250, 200000, 250000, 312500, 390625, 500000, 625000, 781250, 1000000
Offset: 1

Views

Author

Paolo P. Lava, Dec 01 2014

Keywords

Examples

			a(1) = 1;
a(2) = 2 -> 12 /2 = 6;
Now we cannot use 3 as the next term because it does not divide 23.
a(3) = 4 -> 24 / 4 = 6;
a(4) = 5 -> 45 / 5 = 9;
Again, 6, 7, 8 and 9 cannot be used as the next term.
a(5) = 10 -> 510 / 10 = 51;
a(6) = 20 -> 1020 / 20 = 51;
a(7) = 25 -> 2025 / 25 = 81; etc.

Links

Crossrefs

Cf. A171785, A249399, A250745, A250746, A250747.

Programs

  • Maple
    with(numtheory); P:=proc(q) local a,k,n; print(1); a:=1;
for n from 2 to q do if type((a*10^(1+ilog10(n))+n)/n,integer)
then a:=n; print(n); fi; od; end: P(10^12);

A249399 Start with a(1) = 1 then a(n) = smallest number, not already in the sequence, such that a(n) divides concat(a(n-1),a(n)).

Original entry on oeis.org

1, 2, 4, 5, 10, 20, 8, 16, 25, 50, 40, 32, 64, 80, 100, 125, 200, 160, 128, 250, 400, 320, 256, 500, 625, 1000, 800, 640, 512, 1024, 1250, 2000, 1280, 1600, 2500, 3125, 5000, 3200, 2048, 2560, 4000, 6250, 10000, 6400, 4096, 5120, 8000, 10240, 8192, 12500, 15625
Offset: 1

Views

Author

Paolo P. Lava, Dec 01 2014

Keywords

Comments

Like A249398, but without the constraint a(n) > a(n-1).

Examples

			a(1) = 1;
a(2) = 2 -> 12 /2 = 6;
Now we cannot use 3 as the next term because it does not divide 23.
a(3) = 4 -> 24 / 4 = 6;
a(4) = 5 -> 45 / 5 = 9;
Again, 3, 6, 7, 8 and 9 cannot be used as the next term.
a(5) = 10 -> 510 / 10 = 51;
a(6) = 20 -> 1020 / 20 = 51;
a(7) = 8 -> 208 / 8 = 26; etc.

Links

Crossrefs

Cf. A171785, A249398, A250745, A250746, A250747.

Programs

  • Maple
    with(numtheory); P:=proc(q) local a,b,k,n; print(1); a:=1; b:={1};
for k from 1 to q do for n from 1 to q do if nops({n} intersect b)<1
then if type((a*10^(1+ilog10(n))+n)/n,integer)
then a:=n; b:=b union {n}; print(n); break;
fi; fi; od; od; end: P(10^12);

A250745 Start with a(1) = 1; then a(n) = smallest number, not already in the sequence, such that a(n) divides concat(a(1), a(2), ..., a(n)).

Original entry on oeis.org

1, 2, 3, 5, 10, 4, 8, 6, 11, 20, 13, 7, 9, 12, 15, 18, 14, 25, 30, 24, 16, 32, 40, 29, 50, 100, 26, 52, 39, 21, 28, 35, 42, 17, 34, 51, 23, 46, 27, 36, 45, 43, 19, 38, 68, 48, 60, 75, 90, 54, 56, 58, 22, 44, 33, 55, 97, 125, 200, 64, 80, 69, 66, 88, 70, 41, 82
Offset: 1

Views

Author

Paolo P. Lava, Nov 27 2014

Keywords

Comments

Like A171785 but without the constraint a(n) > a(n-1).
Among the first 1000 terms, a(n) = n for n = 1, 2, 3, 15, 170, 577, 759, and the numbers not yet found are 149, 298, 347, 401, 447, 454, 457, 467, 487, 509, etc.
Is this sequence a rearrangement of the natural numbers?

Examples

			a(1) = 1;
a(2) = 2 -> 12 /2 = 6;
a(3) = 3 -> 123 / 3 = 41;
Then we cannot use 4 as the next term because 1234 / 4 = 617 / 2.
a(4) = 5 -> 1235 / 5 = 247;
Again, 4, 6, 7, 8 and 9 cannot be used as the next term.
a(5) = 10 -> 123510 / 10 = 12351;
a(6) = 4 -> 1235104 / 4 = 308776;
a(7) = 8 -> 12351048 / 8 = 1543881; etc.

Links

Crossrefs

Cf. A171785, A240588, A241811, A249398, A249399, A250746, A250747.

Programs

  • Maple
    with(numtheory); P:=proc(q) local a,b,k,n; a:=0; b:={};
for k from 1 to q do for n from 1 to q do if nops({n} intersect b)<1
then if type((a*10^(1+ilog10(n))+n)/n,integer)
then a:=a*10^(1+ilog10(n))+n; b:= b union {n}; print(n); break;
fi; fi; od; od; end: P(10^5);

A250747 Start with a(0) = 0; then a(n) = smallest number not already in the sequence such that a(n) divides concat(a(n), a(n-1), ..., a(0)).

Original entry on oeis.org

0, 1, 2, 3, 5, 10, 6, 9, 13, 26, 15, 18, 30, 431, 73, 67, 134, 7, 14, 21, 35, 29, 58, 127, 27, 39, 43, 70, 11, 22, 19, 38, 95, 190, 2748070932534311, 2768821759897, 5537643519794, 787, 191, 382, 955, 17, 31, 45, 54, 90, 101, 202, 303, 57, 114, 47, 55, 33, 66
Offset: 0

Views

Author

Paolo P. Lava, Nov 28 2014

Keywords

Comments

Like A250746, but without the constraint a(n) > a(n-1).

Examples

			a(0) = 0;
a(1) = 1 -> 10 / 1 = 10;
a(2) = 2 -> 210 / 2 = 105;
a(3) = 3 -> 3210 / 3 = 1070;
Now we cannot use 4 as the next term because 43210 / 4 = 21605 / 2.
a(4) = 5 -> 32105 / 5 = 6421;
Again, we cannot use 4, 6, 7, 8 or 9.
a(5) = 10 -> 1053210 / 10 = 105321.
We still cannot use 4, but 6 is ok.
a(6) = 6 -> 61053210 / 6 = 10175535. Etc.

Links

Crossrefs

Cf. A171785, A240588, A241811, A249398, A249399, A250745, A250746.

Programs

  • Maple
    with(numtheory); P:=proc(q) local a,b,k,n; print(0); print(1); a:=10; b:={0,1};
for k from 1 to q do for n from 1 to q do if nops({n} intersect b)<1
then if type((n*10^(1+ilog10(a))+a)/n,integer)
then a:=n*10^(1+ilog10(a))+a; b:= b union {n}; print(n); break; fi; fi;
od; od; end: P(10^5);

Extensions

More terms from Jon E. Schoenfield, Nov 29 2014
Showing 1-4 of 4 results.

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