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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 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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