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

Author

R. J. Mathar, May 10 2023

Keywords

• nonn

Examples

			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
		

Links

• 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.

Crossrefs

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

Programs

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) ;

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)).