A321537 Write n in base 10, shorten all the runs of successive identical digits by 1.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 11, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 2, 0

Offset: 0

Author

N. J. A. Sloane, Nov 13 2018

Keywords

• nonn
• base

Comments

More than the usual number of terms are shown in order to reach some interesting terms.

All primes vanish except those in A050758.

Examples

			22 -> 2, so a(22)=2 is the first term > 1.
10 in not reached until a(1100) = 10.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 0..10000

Crossrefs

A base-10 analog of A318921.

Cf. A321536, A050758.

Programs

Maple

read("transforms"):
A321537 := proc(n)
    local dgsin,dgsout,pos ;
    dgsin := convert(n,base,10) ;
    dgsout := [] ;
    for pos from 2 to nops(dgsin) do
        if op(pos,dgsin) = op(pos-1,dgsin) then
            dgsout := [op(pos,dgsin),op(dgsout)] ;
        end if;
    end do:
    digcatL(dgsout) ;
end proc: # R. J. Mathar, Nov 14 2018

Mathematica

Array[FromDigits[Join @@ Map[Most, Split@ IntegerDigits@ #]] &, 123] (* Michael De Vlieger, Nov 13 2018 *)

PARI

a(n)={my(v=digits(n)); my(L=List()); for(i=1, #v, my(t=v[i]); if(i>1 && t==v[i-1], listput(L,t))); fromdigits(Vec(L))} \\ Andrew Howroyd, Nov 13 2018

Python

from re import split
def A321537(n):
    return int('0'+''.join(d[:-1] for d in split('(0+)|(1+)|(2+)|(3+)|(4+)|(5+)|(6+)|(7+)|(8+)|(9+)',str(n)) if d != '' and d != None)) # Chai Wah Wu, Nov 13 2018