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Search: id:A147673
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| A147673 |
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a(n)=a(n-2)+prime(n)+8 for n>3, a(0..3)=(0,2,3,10): BRIDGE transform of the primes A000040. |
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+0
2
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| 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
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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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.
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LINKS
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National Science Teachers Association, Quantum CyberTeaser Archive #B205, May/June 1997
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EXAMPLE
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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).
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PROGRAM
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(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))) /* or */ a=[2, 3, 10]; for( n=4, 90, a=concat(a, a[n-2]+prime(n)+8)); a
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CROSSREFS
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Cf. A147672.
Sequence in context: A143609 A066915 A070253 this_sequence A057507 A163467 A143045
Adjacent sequences: A147670 A147671 A147672 this_sequence A147674 A147675 A147676
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KEYWORD
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nonn
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AUTHOR
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M. F. Hasler (MHasler(AT)univ-ag.fr), Nov 10 2008
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