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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.

%I A361170 #37 May 11 2023 01:44:58
%S A361170 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,
%T A361170 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,
%U A361170 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
%N 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.
%H A361170 Mihai Caragiu, Alexandru Zaharescu and Mohammad Zaki, <a href="https://www.pphmj.com/abstract/7973.htm">An analogue of the Proth-Gilbreath conjecture</a>. Far East Journal of Mathematical Sciences, 81(1) (2013), 1-12.
%F A361170 a(n) = T(n,1) where T(1,k) = prime(k), T(n,k) = A006530( T(n-1,k+1) + T(n-1,k)).
%e A361170 The table starts
%e A361170   2  3  5  7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71
%e A361170   5  2  3  3  3  5  3  7 13  5 17 13  7  5  5  7  5  2 23  3
%e A361170   7  5  3  3  2  2  5  5  3 11  5  5  3  5  3  3  7  5 13 11
%e A361170   3  2  3  5  2  7  5  2  7  2  5  2  2  2  3  5  3  3  3 11
%e A361170   5  5  2  7  3  3  7  3  3  7  7  2  2  5  2  2  3  3  7  7
%e A361170   5  7  3  5  3  5  5  3  5  7  3  2  7  7  2  5  3  5  7  3
%e A361170   3  5  2  2  2  5  2  2  3  5  5  3  7  3  7  2  2  3  5  2
%e A361170   2  7  2  2  7  7  2  5  2  5  2  5  5  5  3  2  5  2  7  5
%p A361170 T361170 := proc(n,k)
%p A361170     option remember ;
%p A361170     if n = 1 then
%p A361170         ithprime(k) ;
%p A361170     else
%p A361170         A006530(procname(n-1,k+1)+procname(n-1,k)) ;
%p A361170     end if;
%p A361170 end proc:
%p A361170 A361170 := proc(n)
%p A361170     T361170(n,1) ;
%p A361170 end proc:
%p A361170 seq(A361170(n),n=1..120) ;
%Y A361170 Cf. A006530, A071216 (row n=2).
%K A361170 nonn
%O A361170 1,1
%A A361170 _R. J. Mathar_, May 10 2023