

A239083


The sequence S = a(1), a(2), ... is defined by a(1)=1, if d,e,f are consecutive digits then we do not have d < e < f, and S is always extended with the smallest integer not yet present in S.


19



1, 2, 10, 3, 11, 4, 12, 13, 14, 15, 5, 6, 16, 17, 7, 8, 18, 19, 9, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 200, 201, 121, 122, 130, 202
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OFFSET

1,2


COMMENTS

More than the usual number of terms are given in order to show that the pattern breaks after 120.
Computed by Lars Blomberg.
This is the first (Sa) of a family of 25 similar sequences. For others see
The sequence So (see link) has d > e = f in the definition. It does not have its own entry in the OEIS because it begins with the numbers 1 through 99. Using xy to indicate the numbers from x through y, the sequence So begins like this:
199,101109,120,110112,121,201,113,122130,114,131,202,132140,115,141,
203,142150,116,151,204,152160,117,161,205,162170,118,171,206, 172180,
119,181,207,182191, 208,192199,209, 210,212219,230, 220223,231, 224,232,
301, 225,233240,226,241,227,242, ...
Likewise, the sequence Sw is omitted for a similar reason. It has d = e > f in the definition, and begins 189,99,999,9999,99999,999999,9999999,..., continuing with strings of 9's.
Again, the sequences Sx and Sy are omitted because they are too close to A130571.
Sx (which has d = e >= f) begins
111,20,1219,21,22,30,2329,3133,40,3439,4144,50,4549,5155,60,5659,
6166, 70,6769,7177,80,78,79,8188,90,89,100,9198,101,120,102109,
112119,121,122,300, 123133,400,134144,500,145155,600,156166,700,
167177,800,178188,900,189198,200202, ...
and Sy (d = e = f) begins
111,20,1219,21,22,30,2329,3133,40,3439,4144,50,4549,5155,60,5659,
6166, 70,6769,7177,80,78,79,8188,90,89,91110,112221,223332,334443,
445554,556665, 667776,778887,889899,1001,900989,1002,990998,10031010,...
The sequences Sd, Si, Sl, Sq are omitted because they do not have enough terms to warrant their own entries.


REFERENCES

Eric Angelini, Posting to Sequence Fans Mailing List, Sep 28 2013


LINKS



MATHEMATICA

a[1]=1; a[n_]:=a[n]=Block[{k=1}, While[MemberQ[s=Array[a, n1], k]Or@@(#<#2<#3&@@@Partition[Flatten[IntegerDigits/@Join[s[[2;; ]], {k}]], 3, 1]), k++]; k]; Array[a, 126] (* Giorgos Kalogeropoulos, May 13 2022 *)


PROG

(Python)
is_ok = lambda s: not any(s[i2] < s[i1] < s[i] for i in range(2, len(s)))
terms, appears, digits = [1], {1}, '1'
for i in range(100):
t = 1
while not(t not in appears and is_ok(digits + str(t))):
t += 1
terms.append(t); appears.add(t); digits = digits + str(t)
digits = digits[2:]


CROSSREFS



KEYWORD



AUTHOR



STATUS

approved



