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A154770
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a(n+1) = A154771(a(n)) = sum of all distinct "valid substrings" of a(n); a(1)=10 (least nontrivial choice).
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3
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10, 11, 12, 15, 21, 24, 30, 33, 36, 45, 54, 63, 72, 81, 90, 99, 108, 127, 176, 283, 407, 458, 578, 733, 849, 1003, 1117, 1381, 2044, 2318, 2953, 4397, 5435, 6557, 7964, 9989, 12279, 16572, 26426, 36970, 49970, 67738, 84716, 100181, 111599, 139413, 209606
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| "Valid substrings" means all numbers that appear as substring of n (written in decimal system). Starting values < 10 would yield a constant sequence.
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LINKS
| E. Angelini, Sum of all valid substrings (VS), SeqFan list, Jan 16 2009
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EXAMPLE
| a(1) = 10 has { 0, 1, 10 } as distinct substrings,
a(2) = 0+1+10 = 11 has { 1, 11 } as distinct substrings,
a(3) = 1+11 = 12 has { 1, 2, 12 } as distinct substrings,
a(4) = 1+2+12 = 15 has { 1, 5, 15 } as distinct substrings.
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PROG
| (PARI) A154770( n=2, a=10 ) = { local(d); while( n--, a=vecsort(concat(vector(d=#Str(a), i, vector(d, j, a%10^j)+(d--&!a\=10))), NULL, 8); a*=vector(#a, i, 1)~); a }
print1(a=10); for(i=1, 50, print1(", " a=A154770(, a)))
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CROSSREFS
| Cf. A004207, A154771.
Sequence in context: A046431 A108697 A109279 * A098395 A154328 A112654
Adjacent sequences: A154767 A154768 A154769 * A154771 A154772 A154773
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KEYWORD
| base,easy,nonn
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AUTHOR
| Eric Angelini (eric.angelini(AT)kntv.be) and M. F. Hasler (Maximilian.Hasler(AT)gmail.com), Jan 16 2009
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EXTENSIONS
| The word "distinct" added to definition Jan 19 2009 at the suggestion of Hugo van der Sanden.
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