A178623 Triangle T(n,m) read by rows: T(n,0)= prime(n); T(n,m)=1 if m>=1.

1, 2, 1, 3, 1, 1, 5, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 13, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 17, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 19, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 23, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 29

Offset: 0

Author

Paul Curtz, May 31 2010

Keywords

• nonn
• tabf
• easy
• less

Comments

The sequence reflects a conjecture on the denominator of inverse Bernoulli polynomials in A178340: if the row index is one less than one of the primes in A008578, the row of denominators starts with that prime and contains 1's in the remaining entries.

[Row sums in A178252 are A159069(n+1), unless there is a common factor in numerator and denominator. The row sum over columns with index of the same parity as the row index in the table of fractions of the [x^m] B^{-1}(n,x) in A178252 are: 1, 1, 1/3+1=4/3, 1+1=2, 1/5+2+1=16/5, 1+10/3+1=16/3, 1/7+3+5+1=64/7, 16, 256/9, 256/5, 1024/11, 512/3, 496/13, ... =A084623(n+1)/A000265(n+1).]

Examples

			1;
2,1;
3,1,1;
5,1,1,1,1;
7,1,1,1,1,1,1;
11,1,1,1,1,1,1,1,1,1,1;
13,1,1,1,1,1,1,1,1,1,1,1,1;
17,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1;
19,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1;
23,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1;
29,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1;
		

Crossrefs

Cf. A076274 (row sums).

Formula

T(n,0) = A008578(n+1). T(n,m) =1, 1<=m<=A008578(n+1)-1.