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A258785 Numbers n whose digits match the almost-natural numbers from A007376(n) onwards. 0

%I #15 Dec 10 2016 19:38:47

%S 1,2,3,4,5,6,7,8,9,10,63,3105,43108,77781,367573,13859021,77911127,

%T 911360799,35924813703,74075186297,89012345679,111111111111,

%U 811818896748

%N Numbers n whose digits match the almost-natural numbers from A007376(n) onwards.

%C The almost-natural numbers, A007376, are formed by writing n in base 10 and juxtaposing digits. It is trivially obvious that n = A007376(n) for 1 to 9 and that A007376(10) = 1 and A007376(11) = 0. When n = 63, A007376(63) = 6 and A007376(64) = 3. 63 is therefore the first nontrivial entry in the list.

%C a(24) > 10^12. - _Giovanni Resta_, Jun 10 2015

%C Had A007376 started with 0 instead of 1, this sequence would have been 702, 612052, 1222222, 20987654322, ... - _Giovanni Resta_, Jun 10 2015

%F digits(n,i=1,j) = A007376(n+i-1)

%e digits(63,i=1,2) = A007376(63+i-1)

%e digits(63,i=1) = 6 = A007376(63)

%e digits(63,i=2) = 3 = A007376(64)

%e digits(3105,i=1,4) = A007376(3105+i-1)

%e digits(3105,i=1) = 3 = A007376(3105)

%e digits(3105,i=2) = 1 = A007376(3106)

%e digits(3105,i=3) = 0 = A007376(3107)

%e digits(3105,i=4) = 5 = A007376(3108)

%o (PARI) { b=10; dmx=9; almost=vector(dmx); for(l=1,dmx,almost[l]=l);nmx=b^dmx-1; dn=dmx+1; dig=digits(dn,b); di=1; n=0; while(n<nmx, n++; d=digits(n,b); same=0; for(i=1,#d,if(d[i]==almost[i],same++,i=#d)); if(same==#d,print1(n,", ")); for(i=1,dmx-1,almost[i]=almost[i+1]); almost[dmx]=dig[di]; di++; if(di>#dig, dn++; dig=digits(dn,b); di=1; ); ); }

%Y Cf. A007376, A033307.

%K nonn,base,more

%O 1,2

%A _Anthony Sand_, Jun 10 2015

%E a(22)-a(23) from _Giovanni Resta_, Jun 10 2015

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Last modified March 28 17:25 EDT 2024. Contains 371254 sequences. (Running on oeis4.)