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

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 63, 3105, 43108, 77781, 367573, 13859021, 77911127, 911360799, 35924813703, 74075186297, 89012345679, 111111111111, 811818896748

Offset

1,2

Comments

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.

a(24) > 10^12. - Giovanni Resta, Jun 10 2015

Had A007376 started with 0 instead of 1, this sequence would have been 702, 612052, 1222222, 20987654322, ... - Giovanni Resta, Jun 10 2015

Links

Table of n, a(n) for n=1..23.

Formula

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

Example

digits(63,i=1,2) = A007376(63+i-1)
digits(63,i=1) = 6 = A007376(63)
digits(63,i=2) = 3 = A007376(64)
digits(3105,i=1,4) = A007376(3105+i-1)
digits(3105,i=1) = 3 = A007376(3105)
digits(3105,i=2) = 1 = A007376(3106)
digits(3105,i=3) = 0 = A007376(3107)
digits(3105,i=4) = 5 = A007376(3108)

Prog

(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; ); ); }

Crossrefs

Cf. A007376, A033307.

Sequence in context: A183533 A132576 A161948 * A004861 A178404 A055649

Adjacent sequences: A258782 A258783 A258784 * A258786 A258787 A258788

Keyword

nonn,base,more

Author

Anthony Sand, Jun 10 2015

Extensions

a(22)-a(23) from Giovanni Resta, Jun 10 2015

Status

approved