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A147673
a(n) = a(n-2)+prime(n)+8 for n>3, a(0..3)=(0,2,3,10): BRIDGE transform of the primes A000040.
2
0, 2, 3, 10, 18, 29, 39, 54, 66, 85, 103, 124, 148, 173, 199, 228, 260, 295, 329, 370, 408, 451, 495, 542, 592, 647, 701, 758, 816, 875, 937, 1010, 1076, 1155, 1223, 1312, 1382, 1477, 1553, 1652, 1734, 1839, 1923, 2038, 2124, 2243, 2331, 2462, 2562, 2697, 2799
OFFSET
0,2
COMMENTS
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.
EXAMPLE
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).
PROG
(PARI)
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] ))) }
A147673 = BRIDGE( vector( 20, n, prime(n)))
(PARI)
a=[2, 3, 10]; for( n=4, 90, a=concat(a, a[n-2]+prime(n)+8)); a
CROSSREFS
Cf. A147672.
Sequence in context: A339924 A333673 A070253 * A298345 A057507 A233895
KEYWORD
nonn,changed
AUTHOR
M. F. Hasler, Nov 10 2008
STATUS
approved