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A154770
a(n+1) = A154771(a(n)) = sum of all distinct "valid substrings" of a(n); a(1)=10 (least nontrivial choice).
4
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
OFFSET
1,1
COMMENTS
"Valid substrings" means all numbers that appear as substring of n (written in decimal system). Starting values < 10 would yield a constant sequence.
LINKS
E. Angelini, Sum of all valid substrings (VS), SeqFan list, Jan 16 2009
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.
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)))
CROSSREFS
Sequence in context: A109279 A258744 A219251 * A320601 A305130 A098395
KEYWORD
base,easy,nonn
AUTHOR
Eric Angelini and M. F. Hasler, Jan 16 2009
EXTENSIONS
The word "distinct" added to definition Jan 19 2009 at the suggestion of Hugo van der Sanden.
STATUS
approved