A250745 -id:A250745 - cp's OEIS frontend

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)).

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

Paolo P. Lava, Dec 01 2014

			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.

Paolo P. Lava, Table of n, a(n) for n = 1..100

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

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

Paolo P. Lava, Dec 01 2014

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

			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.

Paolo P. Lava, Table of n, a(n) for n = 1..100

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

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);

A250746 Start with a(0) = 0; then a(n) = smallest number > a(n-1) such that a(n) divides concat(a(n), a(n-1), ..., a(0)).

Original entry on oeis.org

0, 1, 2, 3, 5, 10, 15, 18, 19, 35, 42, 51, 55, 70, 85, 93, 95, 106, 155, 217, 310, 745, 1210, 1342, 3355, 5185, 6222, 6330, 9495, 10413, 11115, 12070, 13774, 34435, 41322, 61983, 68870, 1601065116264571, 2217993924228622, 2324778503347862, 2325380783693255

Offset: 0

Paolo P. Lava, Nov 27 2014

This sequence is infinite. - Robert G. Wilson v, Dec 09 2014

			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; etc.

Robert G. Wilson v, Table of n, a(n) for n = 0..46

Cf. A171785, A240588, A241811, A249398, A249399, A250745, A250747.

with(numtheory); P:=proc(q) local a,k,n; print(0); print(1); a:=10;
for n from 2 to q do if type((n*10^(1+ilog10(a))+a)/n,integer)
then a:=n*10^(1+ilog10(a))+a; print(n);
fi; od; end: P(10^9);

f[lst_List] := Block[{k = lst[[-1]] + 1, id = FromDigits@ Flatten@ IntegerDigits@ Reverse@ lst}, While[ Mod[ id, k] > 0, k++]; Append[lst, k]]; Nest[f, {0}, 36] (* or *)
f[lst_List] := Block[{mn = lst[[-1]], id = FromDigits@ Flatten@ IntegerDigits@ Reverse@ lst}, d = Divisors@ id; Append[lst, Min@ Select[d, # > mn &]]]; Nest[f, {0, 1}, 36] (* Robert G. Wilson v, Dec 08 2014 *)

a(37)-a(40) from Robert G. Wilson v, Dec 08 2014

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

Paolo P. Lava, Nov 28 2014

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

			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.

Jon E. Schoenfield, Table of n, a(n) for n = 0..165

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

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);

More terms from Jon E. Schoenfield, Nov 29 2014

cp's OEIS Frontend

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)).

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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)).

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A250746 Start with a(0) = 0; then a(n) = smallest number > a(n-1) such that a(n) divides concat(a(n), a(n-1), ..., a(0)).

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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)).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple

Extensions