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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 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=1..47.

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

Cf. A004207, A154771.

Sequence in context: A109279 A258744 A219251 * A098395 A207968 A207671

Adjacent sequences:  A154767 A154768 A154769 * A154771 A154772 A154773

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

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Last modified June 27 15:08 EDT 2017. Contains 288790 sequences.