OFFSET
0,2
COMMENTS
When A225402(k) = 0, i.e., k is a term of A352282, then a(k) > a(k+1); 1st example is for k = 17 with a(17) = 115138644385446477 > a(18) = 15138644385446477; otherwise, a(n) < a(n+1).
When n <> k, a(n) coincides with the 'backward concatenation' of A225402(n-1) up to A225402(0), where A225402 is the 10-adic integer x such that x^3 = -1/3 (see table in Example section); when n = k, a(k) must be calculated directly with the definition.
Without "exactly" in the name, terms a'(n) should be also: 1, 7, 77, 477, 6477, 46477, 446477, ..., first difference arrives for n = 17.
There are similar sequences when cubes end with 1, 7, 8 or 9.
EXAMPLE
a(0) = 1 because 1^3 = 1;
a(1) = 7 because 7^3 = 343;
a(2) = 77 because 77^3 = 456533;
a(3) = 477 because 477^3 = 108531333;
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| | a(n) | a'(n) | A225402(n-1) | concatenation |
| n | with "exactly" | without "exactly" | = b(n-1) | b(n-1)...b(0) |
------------------------------------------------------------------------------
1 7 7 7 ...7
2 77 77 7 ...77
3 477 477 4 ...477
............................................................................
15 138644385446477 138644385446477 1 ...138644385446477
16 5138644385446477 5138644385446477 5 ...5138644385446477
17 115138644385446477 15138644385446477 1 ...15138644385446477
18 15138644385446477 15138644385446477 0 ...015138644385446477
19 5015138644385446477 5015138644385446477 5 ...5015138644385446477
------------------------------------------------------------------------------
CROSSREFS
KEYWORD
nonn
AUTHOR
Bernard Schott, Apr 24 2022
STATUS
approved