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 x-y to indicate the numbers from x through y, the sequence So begins like this:
1-99,101-109,120,110-112,121,201,113,122-130,114,131,202,132-140,115,141,
203,142-150,116,151,204,152-160,117,161,205,162-170,118,171,206, 172-180,
119,181,207,182-191, 208,192-199,209, 210,212-219,230, 220-223,231, 224,232,
301, 225,233-240,226,241,227,242, ...
Likewise, the sequence Sw is omitted for a similar reason. It has d = e > f in the definition, and begins 1-89,99,999,9999,99999,999999,9999999,..., 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
1-11,20,12-19,21,22,30,23-29,31-33,40,34-39,41-44,50,45-49,51-55,60,56-59,
61-66, 70,67-69,71-77,80,78,79,81-88,90,89,100,91-98,101,120,102-109,
112-119,121,122,300, 123-133,400,134-144,500,145-155,600,156-166,700,
167-177,800,178-188,900,189-198,200-202, ...
and Sy (d = e = f) begins
1-11,20,12-19,21,22,30,23-29,31-33,40,34-39,41-44,50,45-49,51-55,60,56-59,
61-66, 70,67-69,71-77,80,78,79,81-88,90,89,91-110,112-221,223-332,334-443,
445-554,556-665, 667-776,778-887,889-899,1001,900-989,1002,990-998,1003-1010,...
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
Gleb Ivanov, Table of n, a(n) for n = 1..10000
Eric Angelini, Less than <, Equal to =, Greater than > (see sequence Sa)
Eric Angelini, Less than <, Equal to =, Greater than > [Cached copy, with permission of the author] (see sequence Sa)
MATHEMATICA
a[1]=1; a[n_]:=a[n]=Block[{k=1}, While[MemberQ[s=Array[a, n-1], 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[i-2] < s[i-1] < 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:]
print(terms) # Gleb Ivanov, Dec 04 2021
CROSSREFS
KEYWORD
AUTHOR
Michel Marcus and N. J. A. Sloane, Mar 10 2014
STATUS
approved