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%I #57 Apr 19 2022 15:26:28
%S 4,7,9,14,15,16,17,25,26,27,28,29,35,43,44,45,46,47,55,56,57,58,64,71,
%T 73,74,75,76,77,78,79,83,85,86,87,96,99,107,109,110,111,112,113,117,
%U 123,125,133,139,140,141,142,143,148,151,152,153,154,155,156,157,158
%N Every term is the absolute difference of a prime and a nonprime that is also the sum of their indices.
%C More than one pair of a prime and a nonprime may correspond to some of the terms.
%C Sequence A352707 is read by ascending antidiagonals from array T(n,k). Present sequence is those differences T(n,k) which are on their own antidiagonal number n + k.
%C .
%C Array T(n,k) = abs(prime(n)-nonprime(k))
%C n\k| 1 4 6 8 9 ...
%C -----------------------
%C 2 | 1 2 4 6 7 ...
%C 3 | 2 1 3 5 6 ...
%C 5 | 4 1 1 3 4 ...
%C 7 | 6 3 1 1 2 ...
%C 11 | 10 7 5 3 2 ...
%C 13 | 12 9 7 5 4 ...
%C 17 | 16 13 11 9 8 ...
%C 19 | 18 15 13 11 10 ...
%C 23 | 22 19 17 15 14 ...
%C . | . . . . .
%F Sums x + y for which x + y = abs(prime(x) - nonprime(y)), for some x and y.
%e 7 is a term because the 5th prime 11 minus the 2nd nonprime 4 equals 7 and that is also 5 + 2.
%e 9 is a term because the 2nd prime 3 minus the 7th nonprime 12 equals -9 whose absolute value 9 is also 2 + 7.
%e 4 is a term because the 3rd prime 5 minus the 1st nonprime 1 equals 4 that is also 3 + 1. The absolute value of the 1st prime 2 minus the 3rd nonprime 6 also equals 4 that is 1 + 3, so this pair, too, makes 4 a term of this sequence.
%Y Cf. A000040, A018252, A352707 (table T).
%K nonn
%O 1,1
%A _Tamas Sandor Nagy_, Apr 17 2022
%E More terms from _Hugo Pfoertner_, Apr 17 2022
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