A361170 The leading column of the table of primes in the top row and subsequent rows defined by the GPF of Pascal-alike sums of previous rows.

2, 5, 7, 3, 5, 5, 3, 2, 3, 3, 2, 7, 3, 2, 7, 3, 5, 2, 7, 3, 5, 3, 5, 5, 3, 2, 7, 7, 7, 5, 7, 5, 2, 7, 7, 3, 5, 7, 3, 2, 2, 2, 2, 7, 3, 5, 3, 3, 2, 3, 2, 2, 3, 2, 7, 3, 2, 7, 7, 5, 5, 7, 3, 2, 3, 3, 2, 5, 2, 7, 7, 3, 5, 3, 2, 2, 2, 2, 5, 2, 2, 3, 3, 2, 2, 2, 2, 5, 5, 2, 2, 3, 2, 2

Offset

1,1

Links

Table of n, a(n) for n=1..94.

Mihai Caragiu, Alexandru Zaharescu and Mohammad Zaki, An analogue of the Proth-Gilbreath conjecture. Far East Journal of Mathematical Sciences, 81(1) (2013), 1-12.

Formula

a(n) = T(n,1) where T(1,k) = prime(k), T(n,k) = A006530( T(n-1,k+1) + T(n-1,k)).

Example

The table starts
  2  3  5  7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71
  5  2  3  3  3  5  3  7 13  5 17 13  7  5  5  7  5  2 23  3
  7  5  3  3  2  2  5  5  3 11  5  5  3  5  3  3  7  5 13 11
  3  2  3  5  2  7  5  2  7  2  5  2  2  2  3  5  3  3  3 11
  5  5  2  7  3  3  7  3  3  7  7  2  2  5  2  2  3  3  7  7
  5  7  3  5  3  5  5  3  5  7  3  2  7  7  2  5  3  5  7  3
  3  5  2  2  2  5  2  2  3  5  5  3  7  3  7  2  2  3  5  2
  2  7  2  2  7  7  2  5  2  5  2  5  5  5  3  2  5  2  7  5

Maple

T361170 := proc(n, k)
    option remember ;
    if n = 1 then
        ithprime(k) ;
    else
        A006530(procname(n-1, k+1)+procname(n-1, k)) ;
    end if;
end proc:
A361170 := proc(n)
    T361170(n, 1) ;
end proc:
seq(A361170(n), n=1..120) ;

Crossrefs

Cf. A006530, A071216 (row n=2).

Sequence in context: A361130 A361128 A309200 * A097964 A133133 A024710

Adjacent sequences: A361167 A361168 A361169 * A361171 A361172 A361173

Keyword

nonn

Author

R. J. Mathar, May 10 2023

Status

approved