A145280 -id:A145280 - cp's OEIS frontend

A145279 Fecundity of n-th Fibonacci number.

0, 10, 10, 9, 9, 1, 7, 7, 5, 2, 1, 3, 1, 5, 8, 0, 5, 2, 1, 3, 1, 0, 1, 1, 7, 0, 2, 3, 3, 5, 0, 1, 0, 5, 0, 1, 0, 5, 0, 1, 0, 0, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 2, 1, 3, 5, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0

Offset: 0

Paolo P. Lava and Giorgio Balzarotti, Oct 06 2008

Subset of A070562. After the 184th Fibonacci number 127127879743834334146972278486287885163, the fecundity is equal to zero.

The indices of Fibonacci numbers whose fecundity is not zero are {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 17, 18, 19, 20, 22, 23, 24, 26, 27, 28, 29, 31, 33, 35, 37, 39, 42, 43, 53, 54, 55, 56, 57, 58, 78, 80, 85, 87, 97, 125, 184}. - Robert G. Wilson v, Jun 27 2010

			Fib(6)=8 -> 8+8=16 -> 16+1*6=22 -> 22+2*2=26 -> 26+2*6=38 -> 38+3*8=62 -> 62+6*2=74 -> 74+7*4=102 -> 7 steps to reach a zero digit.

Cf. A070562, A145280.

P:=proc(i) local a,b,c,d,f,g,ok,k,w,n; d:=0; f:=1; print(d); print(10); for n from 0 by 1 to i do a:=d+f; g:=f; f:=a; d:=g; b:=1; c:=0; ok:=1; while ok=1 do k:=a; w:=1; while k>0 do w:=w*(k-(trunc(k/10)*10)); k:=trunc(k/10); od; if w=0 then ok:=0; else c:=c+1; a:=a+w; fi; od; print(c); od; end: P(200);

f[n_] := Length@ FixedPointList[ # + Times @@ IntegerDigits@# &, n] - 2; Array[f@ Fibonacci@# &, 105, 0] (* Robert G. Wilson v, Jun 27 2010 *)

A225544 a(n) begins the earliest chain of exactly n distinct primes such that any term in the chain equals the previous term increased by the product of its digits.

Original entry on oeis.org

2, 29, 23, 347, 293, 239, 57487, 486193, 1725121513, 1221261395831, 28549657193411

Offset: 1

Giovanni Resta, May 10 2013

A chain ends either at a composite number, or at a prime which contains a zero, since the subsequent primes in the chain are identical.

			23 starts the earliest chain of length 3, since 23+2*3 = 29, 29+2*9 = 47 and 47+4*7 = 75, where the first 3 terms are distinct and prime, so a(3) = 23. The last distinct term in the chain starting at 1725121513 is the prime 1725980623 which contains a zero and thus generates itself.

Cf. A090009, A145280.

seq = 0*Range[8]; p = 2; While[p < 500000, v = Length@ NestWhileList[# + Times @@ IntegerDigits@# &, p, PrimeQ@#2 && #1 != #2 &, 2] - 1; If[ seq[[v]] == 0, seq[[v]] = p]; p = NextPrime@p]; seq

cp's OEIS Frontend

A145279 Fecundity of n-th Fibonacci number.

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