OFFSET
1,1
COMMENTS
The sum of the reciprocals of this sequence diverges; it grows as log log n, just as the sum of the reciprocals of the primes does. - Franklin T. Adams-Watters, Mar 30 2006
FORMULA
The digits of Pi are added d_1+d_2..d_i and the prime whose index is the i-th sum is chosen. E.g. for Pi = 3.14149265358979... the first Pisumprime is prime (3) the second is prime(4), 3rd prime(8) etc. Let d_1, d_2, ..d_i be the expansion of the decimal digits of Pi. Then Pisumprime(n) = prime(d_1), prime (d_1+d_2), ...prime(sum(d_i, i=1..n)). This can be generalized to pisumprime(n, z) where z is the nesting level of prime(x). for z=1 we have prime() for z=2 we have prime (prime(x)), z=3 prime(prime(prime(x))) etc.
MATHEMATICA
Prime[#]&/@Accumulate[RealDigits[Pi, 10, 40][[1]]] (* Harvey P. Dale, Sep 30 2012 *)
PROG
(PARI) \\ pi digit sum index primes; pisump.gp Primes whose index is the sequential sum of digits of pi
{ pisump(n) = default(realprecision, 100000); p = Pi/10; default(realprecision, 28); sr=0; s=0; for(x=1, n, d = p*10; d1=floor(d); s+=d1; p = frac(d); d = p*10; p2=prime(s); sr+=1/p2+0.; print1(p2, ", "); ); print(" "); print(sr); }
CROSSREFS
KEYWORD
easy,nonn,base
AUTHOR
Cino Hilliard, Nov 16 2002
EXTENSIONS
Edited by T. D. Noe, Jun 24 2009
STATUS
approved