cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A224780 Strings of ascending digits in A007376.

Original entry on oeis.org

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

Views

Author

Dave Durgin, Apr 17 2013

Keywords

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.

Examples

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

Programs

  • 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