A224780 Strings of ascending digits in A007376.

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

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 * A367595 A277057 A180408

Adjacent sequences: A224777 A224778 A224779 * A224781 A224782 A224783

Keyword

nonn,base

Author

Dave Durgin, Apr 17 2013

Status

approved