A154770 a(n+1) = A154771(a(n)) = sum of all distinct "valid substrings" of a(n); a(1)=10 (least nontrivial choice).

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

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 * A320601 A305130 A098395

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