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Write n in base 10, shorten all the runs of successive identical digits by 1.
3

%I #24 Nov 29 2018 10:38:38

%S 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,

%T 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,

%U 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

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

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

%C All primes vanish except those in A050758.

%H Chai Wah Wu, <a href="/A321537/b321537.txt">Table of n, a(n) for n = 0..10000</a>

%e 22 -> 2, so a(22)=2 is the first term > 1.

%e 10 in not reached until a(1100) = 10.

%p read("transforms"):

%p A321537 := proc(n)

%p local dgsin,dgsout,pos ;

%p dgsin := convert(n,base,10) ;

%p dgsout := [] ;

%p for pos from 2 to nops(dgsin) do

%p if op(pos,dgsin) = op(pos-1,dgsin) then

%p dgsout := [op(pos,dgsin),op(dgsout)] ;

%p end if;

%p end do:

%p digcatL(dgsout) ;

%p end proc: # _R. J. Mathar_, Nov 14 2018

%t Array[FromDigits[Join @@ Map[Most, Split@ IntegerDigits@ #]] &, 123] (* _Michael De Vlieger_, Nov 13 2018 *)

%o (Python)

%o from re import split

%o def A321537(n):

%o 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

%o (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

%Y A base-10 analog of A318921.

%Y Cf. A321536, A050758.

%K nonn,base

%O 0,23

%A _N. J. A. Sloane_, Nov 13 2018