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

Author

Eric Angelini and M. F. Hasler, Jan 16 2009

Keywords

• base
• easy
• nonn

Comments

"Valid substrings" means all numbers that appear as substring of n (written in decimal system). Starting values < 10 would yield a constant sequence.

Examples

			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.
		

Links

• E. Angelini, Sum of all valid substrings (VS), SeqFan list, Jan 16 2009

Crossrefs

Cf. A004207, A154771.

Programs

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)))

Extensions

The word "distinct" added to definition Jan 19 2009 at the suggestion of Hugo van der Sanden.