A375232
Two terms that contain the digit "d" are always separated by "d" terms that do not contain the digit "d". This is the lexicographically earliest sequence of distinct nonnegative integers with this property.
Original entry on oeis.org
0, 10, 20, 100, 30, 102, 40, 101, 203, 105, 60, 1024, 300, 107, 200, 150, 304, 1026, 80, 109, 230, 10457
Offset: 1
As we start the sequence with a(1) = 0, the digit 0 must be present in every term of the sequence.
We extend it now with a(2) = 10 as 10 is the smallest integer not present that contains the digit 0.
The next term will be a(3) = 20 as 20 is the smallest integer not present that contains the digit 0.
The next term will be a(4) = 100 as 100 is the smallest integer not present that contains both the digits 0 and 1.
The next term will be a(5) = 30 as 30 is the smallest integer not present that contains the digit 0.
The next term will be a(6) = 102 as 102 is the smallest integer not present that contains the digits 0, 1 and 2.
The next term will be a(7) = 40 as 40 is the smallest integer not present that contains the digit 0.
The next term will be a(8) = 101 as 101 is the smallest integer not present that contains both the digits 0 and 1.
Etc.
a(14) and successive terms computed by Michael S. Branicky.
A284651
Lexicographically earliest sequence of unique numbers such that for each digit "d" exactly one of the gaps to the neighboring digits "d" is equal to d, and no gap is smaller than d.
Original entry on oeis.org
1, 2, 13, 24, 5, 3, 6, 7, 4, 8, 52, 9, 62, 73, 18, 132, 91, 21, 34, 25, 32, 46, 15, 17, 23, 621, 31, 72, 41, 213, 42, 53, 26, 47, 58, 94, 63, 171, 38, 19, 12, 35, 27, 36, 85, 14, 176, 248, 29, 51, 71, 265, 28, 97, 16, 100, 48, 37, 54, 39, 625, 724, 86, 294, 200, 78, 45, 161, 475, 92, 61, 214, 57, 89, 415, 137, 68, 300
Offset: 1
The first 16 terms of this variant are 1, 2, 13, 24, 5, 3, 6, 7, 4, 8, 52, 9, 62, 73, 18, 132.
The first 16 terms of the orig seq are 1, 2, 13, 24, 5, 3, 6, 7, 4, 8, 52, 9, 62, 73, 18, 131.
The difference is in the last digit of the last term (131 becomes here 132): in the original sequence the first digit "1" of the term "131" is twice at a gap of 1 digit from another "1" (there is indeed a gap of 1 digit between the first "1" of "131" and the "1" of "18" AND there is also a gap of 1 digit between the first and the second "1" of "131"). This is forbidden in this variant, whatever digit "d" you pick: if your digit "d" is at a gap of d from another "d", it cannot be at the same gap of another "d".
A365513
Lexicographically earliest permutation of the nonnegative integers with the property that the successive sizes of the gaps between nonprime terms and the successive sizes of the gaps between nonprime digits show the same pattern.
Original entry on oeis.org
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 11, 15, 16, 18, 20, 21, 13, 22, 24, 25, 26, 17, 27, 19, 28, 30, 23, 29, 31, 37, 32, 41, 43, 47, 33, 34, 53, 59, 61, 35, 36, 67, 38, 71, 39, 73, 79, 83, 40, 89, 42, 97, 101, 103, 107, 44, 45, 46, 109, 48
Offset: 1
Sequence read as a succession of terms:
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 11, 15, 16, ...
The gaps between nonprime terms are of size:
0, 2, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, ...
Sequence read as a succession of digits:
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 0, 1, 2, 1, 4, 1, 1, 1, 5, 1, 6, ...
The gaps between nonprime digits are of size:
0, 2, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, ...
- Eric Angelini, Same gaps pattern, Personal blog "Cinquante signes", Sept 2023.
- Eric Angelini, Same gaps pattern, Personal blog "Cinquante signes", Sept 2023. [Cached copy]
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a[1]=0;a[n_]:=a[n]=(k=1;While[MemberQ[s=Array[a,n-1],k]||PrimeQ@k!= PrimeQ[Flatten[IntegerDigits/@Join[s,{k}]][[n]]],k++];k);Array[a,70] (* Giorgos Kalogeropoulos, Sep 07 2023 *)
Original entry on oeis.org
0, 10, 20, 100, 30, 102, 40, 101, 203, 105, 60, 1024, 300, 107, 200, 150, 304, 1026, 80, 109, 230, 10457, 0, 120, 306, 110, 204, 1058, 303, 10279, 0, 1046, 302, 501, 0, 201, 3048, 170, 206, 1059, 330, 1042, 0, 1000, 320, 105678, 400, 210, 3000, 190, 202, 1045, 360, 1027, 800, 1001, 2034, 510, 0, 10269
Offset: 1
The finite sequence A375232 ends with 80, 109, 230, 10457. If we extend it with a(23) = 0, we can compute a(24) = 120, a(25) = 306 then 110, 204, 1058, 303 and 10279. No more integers are available at that stage. But, again, we can extend the sequence with a(31) = 0, then a(32) = 1046 and 302, 501, 0, 201, 3048, 170, etc.
A repeated single 0 is counted as a term of the sequence.
Showing 1-4 of 4 results.
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