This site is supported by donations to The OEIS Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A238986 Ground Pyramidalized Numbers: Write the decimal digits of 'n' (a nonnegative integer) and take successive absolute differences ("pyramidalization"), then sum all digits of each level of the pyramid. If total is greater than 9, repeat the process until result is between 0 and 9, which is 'a(n)' (0 <= a(n) <= 9). 1
 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 2, 2, 4, 6, 8, 2, 4, 8, 4, 4, 4, 4, 4, 6, 8, 2, 4, 8, 4, 4, 6, 6, 6, 6, 8, 2, 4, 8, 4, 4, 8, 8, 8, 8, 8, 2, 4, 8, 4, 4, 2, 2, 2, 2, 2, 2, 4, 8, 4, 4 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS A given nonnegative integer 'n' is decomposed to its digits and the absolute differences between the digits are taken, then the differences between differences between digits (and so on, until the top of the "gap-pyramid" is reached - we could call this process "pyramidalization"). If the sum 's(n)' of the resulting digits is 0 <= s(n) <= 9, it's 'a(n)'; if greater than 9, the same process is applied to the result, and to the subsequent result if necessary, and so on, until the result is smaller than 10. LINKS Giovanni Resta, Table of n, a(n) for n = 0..10000 FORMULA a(n)=n, if 0<=n<=9; b'(n)=n-9*floor(n/10)+|-n+11*floor(n/10)|, if 10<=n<=99;   b'(n)=a(n), if 0<=b'(n)<=9;   else, b''(n)=b'(n)-9*floor(b'(n)/10)+|-b'(n)+11*floor(b'(n)/10)|;   b''(n)=a(n), if 0<=b''(n)<=9;   else, b'''(n)=... c'(n)=n-9*floor(n/10)-9*floor(n/100)+|-floor(n/10)+11*floor(n/100)|+|-n+11*floor(n/10)-10*floor(n/100)|+||-floor(n/10)+11*floor(n/100)|-|-n+11*floor(n/10)-10*floor(n/100)||, if 100<=n<=999.   c'(n)=a(n), if 0<=c'(n)<=9;   else, if 10<=c'(n)<=99, c''(n)=c'(n)-9*floor(c'(n)/10)+|-c'(n)+11*floor(c'(n)/10)|;                           c''(n)=a(n), if 0<=c''(n)<=9                           else, ... EXAMPLE If n=364, a(364)=4, for... . ____1 __3_:_2__ -->b'(364)=3+6+4+|3-6|+|6-4|+||3-6|-|6-4||=3+6+4+3+2+1=19>9 3_:_6_:_4 . __8 1_:_9  --> b''(364)=1+9|1-9|=1+9+8=18>9 . __7 1_:_8 --> b'''(364)=1+8+|1-8|=1+8+7=16>9 . __5 1_:_6 --> b''''(364)=1+6+|1-6|=1+6+5=12>9 . __1 1_:_2 --> b'''''(364)=1+2+|1-2|=1+2+1=4=a(364) MATHEMATICA a[n_] := If[n < 10, n, Block[{d = IntegerDigits@ n, s}, s = Total@ d; While[Length@ d > 1, d = Abs@ Differences@ d; s += Total@d]; If[s < 10, s, a@s]]]; a /@ Range[0, 99] (* Giovanni Resta, Mar 16 2014 *) CROSSREFS Cf. A227876. The pyramidalization process is applied and reapplied to each term until the result reaches its "ground limit". Cf. A007318. The pyramidalization process relates to Pascal's Triangle because it is done in the opposite direction (towards the top instead of the base), using the contrary operation (absolute difference instead of sum of the prior terms). Sequence in context: A138795 A297233 A177895 * A227876 A276716 A189506 Adjacent sequences:  A238983 A238984 A238985 * A238987 A238988 A238989 KEYWORD nonn,base,uned AUTHOR Filipi R. de Oliveira, Mar 07 2014 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 22 16:59 EDT 2019. Contains 327311 sequences. (Running on oeis4.)