login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 * 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 1 23:44 EST 2022. Contains 358485 sequences. (Running on oeis4.)