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A258785 Numbers n whose digits match the almost-natural numbers from A007376(n) onwards. 0
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 63, 3105, 43108, 77781, 367573, 13859021, 77911127, 911360799, 35924813703, 74075186297, 89012345679, 111111111111, 811818896748 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 22 08:00 EDT 2019. Contains 328315 sequences. (Running on oeis4.)