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%I #21 Oct 22 2023 20:32:19
%S 2,3,15,16,36,37,39,40,46,47,54,55,55,56,73,74,102,103,107,108,110,
%T 111,118,119,129,130,160,161,164,165,184,185,187,188,194,195,199,200,
%U 218,219,239,240,271,272,272,273,291,292,339,340,358,359,387,388,419,420
%N Twin prime gaps: Pairs k, k+1 such that f(k) = f(k+1), where f is the prime gaps function given by f(m) = prime(m+1)-prime(m) and prime(m) denotes the m-th prime.
%C Each pair of terms yields a triple of primes in arithmetic progression; e.g., 2,3 yields the prime triple 3,5,7.
%F a(2*n-1) = A064113(n); a(2*n) = A064113(n) + 1. - _Andrew Howroyd_, Oct 22 2023
%e 2,3 is a twin prime gap since f(2) = f(3) = 2. 54,55 is a twin prime gap since f(54) = f(55) = 6.
%t (* to find the smaller number in each twin prime gap *)
%t f[n_] := Prime[n + 1] - Prime[n]; Select[Range[1, 10^3], f[ # ] == f[ # + 1] &]
%Y Cf. A001223 (f), A064113.
%K easy,nonn,tabf
%O 1,1
%A _Joseph L. Pe_, Jan 03 2002
%E More terms from _Jason Earls_, Jan 05 2002
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