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%I #12 Nov 03 2024 02:15:47
%S 0,2,3,10,18,29,39,54,66,85,103,124,148,173,199,228,260,295,329,370,
%T 408,451,495,542,592,647,701,758,816,875,937,1010,1076,1155,1223,1312,
%U 1382,1477,1553,1652,1734,1839,1923,2038,2124,2243,2331,2462,2562,2697,2799
%N a(n) = a(n-2)+prime(n)+8 for n>3, a(0..3)=(0,2,3,10): BRIDGE transform of the primes A000040.
%C The BRIDGE transform of an increasing sequence is defined in A147672. The name comes from the puzzle "Crossing the bridge", cf. link, example and A147672.
%H National Science Teachers Association, <a href="https://www.math.uni-bielefeld.de/~sillke/PUZZLES/quantum/bridgarc.html">Quantum CyberTeaser Archive #B205, May/June 1997</a>
%e a(4)=18=3+2+7+3+3 is the time required to cross the bridge for a boy, his sister, his father and his mother if they require 2,3,5,7 minutes, respectively, to cross the bridge individually (using the moves B+G,B,M+F,G,B+G).
%o (PARI)
%o BRIDGE( a )={ local( s=vector(#a),t ); vector( #a, n, t=vecsort( vecextract( a, 2^n-1 )); t[n]+if( n>3, t[1]+2*t[2]+BRIDGE( vecextract( t,2^(n-2)-1 ))[n-2], if(n==3, t[1]+t[2] ))) }
%o A147673 = BRIDGE( vector( 20, n, prime(n)))
%o (PARI)
%o a=[2,3,10]; for( n=4, 90, a=concat(a,a[n-2]+prime(n)+8));a
%Y Cf. A147672.
%K nonn
%O 0,2
%A _M. F. Hasler_, Nov 10 2008