A362064 Lexicographically earliest sequence of distinct positive integers such that the digit "1" is neither present in a(n) nor in a(n) + a(n+1).

2, 3, 4, 5, 20, 6, 22, 7, 23, 9, 24, 8, 25, 27, 26, 28, 29, 30, 32, 33, 34, 35, 37, 36, 38, 39, 40, 42, 43, 44, 45, 47, 46, 48, 49, 50, 200, 52, 202, 53, 203, 54, 204, 55, 205, 57, 206, 56, 207, 58, 208, 59, 209, 60, 220, 62, 222, 63, 223, 64, 224, 65, 225, 67

Offset: 1

Author

Eric Angelini and Cécile Angelini, Apr 07 2023

Keywords

• base
• nonn

Examples

			2 + 3 = 5; 3 + 4 = 7; 4 + 5 = 9; but as 5 + 6 = 11 we cannot use 6 nor 7 (sum 12), 8 (sum 13) and 9 (sum 14); we cannot use the integers 10 to 19 (as a 1 is present in them), so a(5) = 20 as 5 + 20 = 25, etc.
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A052383, A299957.

Programs

Python

from itertools import islice
def jump1(n):
    s = str(n)
    return n if "1" not in s else int(s[:(i:=s.index("1"))]+"2"+"0"*(len(s)-i-1))
def agen(): # generator of terms
    an, aset, mink = 2, {2}, 3
    while True:
        yield an
        k = mink
        while k in aset or "1" in str(an+k): k = jump1(k+1)
        an = k
        aset.add(an)
        while mink in aset: mink = jump1(mink+1)
print(list(islice(agen(), 64))) # Michael S. Branicky, Apr 07 2023

Extensions

a(27) and beyond from Michael S. Branicky, Apr 07 2023