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.
%I A377033 #9 Dec 16 2024 07:33:04
%S A377033 4,6,2,8,2,0,9,1,-1,-1,10,1,0,1,2,12,2,1,1,0,-2,14,2,0,-1,-2,-2,0,15,
%T A377033 1,-1,-1,0,2,4,4,16,1,0,1,2,2,0,-4,-8,18,2,1,1,0,-2,-4,-4,0,8,20,2,0,
%U A377033 -1,-2,-2,0,4,8,8,0,21,1,-1,-1,0,2,4,4,0,-8,-16,-16
%N A377033 Array read by antidiagonals downward where A(n,k) is the n-th term of the k-th differences of the composite numbers (A002808).
%C A377033 Row n is the k-th differences of A002808 = the composite numbers.
%F A377033 A(i,j) = Sum_{k=0..j} (-1)^(j-k) binomial(j,k) A002808(i+k).
%e A377033 Array begins:
%e A377033 n=1: n=2: n=3: n=4: n=5: n=6: n=7: n=8: n=9:
%e A377033 ----------------------------------------------------------
%e A377033 k=0: 4 6 8 9 10 12 14 15 16
%e A377033 k=1: 2 2 1 1 2 2 1 1 2
%e A377033 k=2: 0 -1 0 1 0 -1 0 1 0
%e A377033 k=3: -1 1 1 -1 -1 1 1 -1 -1
%e A377033 k=4: 2 0 -2 0 2 0 -2 0 2
%e A377033 k=5: -2 -2 2 2 -2 -2 2 2 -2
%e A377033 k=6: 0 4 0 -4 0 4 0 -4 -1
%e A377033 k=7: 4 -4 -4 4 4 -4 -4 3 10
%e A377033 k=8: -8 0 8 0 -8 0 7 7 -29
%e A377033 k=9: 8 8 -8 -8 8 7 0 -36 63
%e A377033 Triangle begins:
%e A377033 4
%e A377033 6 2
%e A377033 8 2 0
%e A377033 9 1 -1 -1
%e A377033 10 1 0 1 2
%e A377033 12 2 1 1 0 -2
%e A377033 14 2 0 -1 -2 -2 0
%e A377033 15 1 -1 -1 0 2 4 4
%e A377033 16 1 0 1 2 2 0 -4 -8
%e A377033 18 2 1 1 0 -2 -4 -4 0 8
%e A377033 20 2 0 -1 -2 -2 0 4 8 8 0
%e A377033 21 1 -1 -1 0 2 4 4 0 -8 -16 -16
%t A377033 nn=9;
%t A377033 t=Table[Take[Differences[NestList[NestWhile[#+1&, #+1,PrimeQ]&,4,2*nn],k],nn],{k,0,nn}]
%Y A377033 Initial rows: A002808, A073783, A073445.
%Y A377033 The version for primes is A095195 or A376682.
%Y A377033 A version for partitions is A175804, cf. A053445, A281425, A320590.
%Y A377033 Triangle row-sums are A377034, absolute version A377035.
%Y A377033 Column n = 1 is A377036, for primes A007442 or A030016.
%Y A377033 First position of 0 in each row is A377037.
%Y A377033 Other arrays of differences: A095195 (prime), A376682 (noncomposite), A377033 (composite), A377038 (squarefree), A377046 (nonsquarefree), A377051 (prime-power).
%Y A377033 A000040 lists the primes, differences A001223, seconds A036263.
%Y A377033 A008578 lists the noncomposites, differences A075526.
%Y A377033 Cf. A065310, A065890, A084758, A173390, A350004, A376602 (zero), A376603 (nonzero), A376651 (positive), A376652 (negative), A376680.
%K A377033 sign,tabl
%O A377033 0,1
%A A377033 _Gus Wiseman_, Oct 17 2024