A130720 - OEIS

%I #13 Jan 27 2014 16:24:00

%S 10,20,33,49,35,63,57,38,19,108,116,124,132,140,715,1650,117,1800,819,

%T 2021,1221,1422,923,2425,925,2601,279,288,297,306,315,324,333,342,351,

%U 360,237,3038,1339,3406,4130,2142,1443,4410,4575,2046,1475,4867,4495

%N Summation of a sequence of sequential numbers containing the first term as a substring.

%H Reinhard Zumkeller, <a href="/A130720/b130720.txt">Table of n, a(n) for n = 1..10000</a>

%F For each counting number i, what is the next number N such that N is the sum of i and the next consecutive counting numbers until N contains i as a substring.

%e a(2)=20 because 2+3+4+5+6=20 and 2 is a substring of 20.

%e a(16)=1650 because 16+17+18+...+59=1650 and 16 is a substring of 1650.

%t f[n_]:=Module[{idn=IntegerDigits[n],len=IntegerLength[n],cl = Rest[ Accumulate[ Range[n, n+100]]]}, Select[cl,MemberQ[Partition[ IntegerDigits[ #],len,1],idn]&,1]]; Flatten[Array[f,50]] (* _Harvey P. Dale_, Jan 18 2012 *)

%o (Haskell)

%o import Data.List (find, isInfixOf)

%o import Data.Maybe (fromJust)

%o a130720 n = fromJust $ find ((show n `isInfixOf`) . show) $

%o                             tail $ scanl1 (+) [n..]

%o -- _Reinhard Zumkeller_, Oct 03 2012

%K easy,nice,nonn,look

%O 1,1

%A _Gil Broussard_, Jul 03 2007