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.

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.

Links

G. C. Greubel, Table of n, a(n) for n = 0..5000

National Science Teachers Association, Quantum CyberTeaser Archive #B205, May/June 1997

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).

Mathematica

A147673[n_]:= A147673[n]= If[n<4, Fibonacci[n]*Fibonacci[n+2], A147673[n-2] +Prime[n] +8];
Table[A147673[n], {n, 0, 70}] (* G. C. Greubel, Dec 02 2025 *)

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
(Magma)
A147673:= function(n)
   if n le 3 then return Fibonacci(n)*Fibonacci(n+2);
   else return $$(n-2) +NthPrime(n) +8;
   end if;
end function;
[A147673(n): n in [0..70]]; // G. C. Greubel, Dec 02 2025
(SageMath)
def A147673(n):
    if n<4: return (0, 2, 3, 10)[n]
    else: return A147673(n-2) +nth_prime(n) +8
print([A147673(n) for n in range(71)]) # G. C. Greubel, Dec 02 2025

Crossrefs

Cf. A147672.

Sequence in context: A339924 A333673 A070253 * A298345 A057507 A233895

Adjacent sequences: A147670 A147671 A147672 * A147674 A147675 A147676

Keyword

nonn

Author

M. F. Hasler, Nov 10 2008

Status

approved