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A224780 Strings of ascending digits in A007376. 0
123456789, 12, 12, 23, 23, 34, 34, 45, 45, 56, 56, 67, 67, 78, 78, 89, 89, 12, 12, 12, 123, 12, 12, 12, 12, 12, 12, 34, 45, 56, 67, 78, 89, 12, 12, 12, 23, 23, 23, 123, 23, 234, 23, 23, 23, 23, 23, 12, 45, 12, 56, 12, 67, 12, 78, 12, 89, 12, 23, 123, 23, 23, 23, 34, 34, 34, 34, 234, 34, 345, 34, 34, 34, 34, 23, 56, 23, 67, 23, 78, 23, 89 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

We sample each digit in A007376 in turn; accept the longest string for which A(n+1)-A(n)=1, A(n+2)-A(n+1)=1 and so on.

We recognize only strings of length >=2 and not strings with leading zeros.

Series is infinite, but there are only 36 possible consecutive strings: 12, 123, 1234,...,123456789 (eight beginning with 1), 23, 234, 2345,...,23456789 (seven beginning with 2) and so on.

LINKS

Table of n, a(n) for n=1..82.

EXAMPLE

The 1st five terms imbedded in A007376 in brackets: [123456789]1011[12]13141516171819202[12]2[23]24252627282930313[23]

MAPLE

A007376 := [] :

for n from 1 to 400 do

    nb := convert(n, base, 10) ;

    A007376 := [op(A007376), op(ListTools[Reverse](nb))] ;

end do:

str := 1 :

while true do

    for a from 1 do

        if op(str+a, A007376) <> 1+op(str+a-1, A007376) then

            break;

        end if;

    end do:

    L := ListTools[Reverse]([op(str..str+a-1, A007376)]) ;

    if nops(L) > 1 and op(-1, L) > 0 then

        add( op(i, L)*10^(i-1), i=1..nops(L)) ;

        printf("%d, ", %) ;

    end if;

    str := str+a ;

end do: # R. J. Mathar, Apr 26 2013

CROSSREFS

Sequence in context: A172888 A172917 A068247 * A277057 A180408 A050289

Adjacent sequences:  A224777 A224778 A224779 * A224781 A224782 A224783

KEYWORD

nonn,base

AUTHOR

Dave Durgin, Apr 17 2013

STATUS

approved

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Last modified July 27 04:53 EDT 2017. Contains 289841 sequences.