|
| |
|
|
A076787
|
|
Pisumprimes: prime(k), where k is the sum of the first n digits of Pi.
|
|
2
|
|
|
|
5, 7, 19, 23, 43, 83, 97, 127, 151, 167, 193, 239, 283, 337, 389, 409, 421, 439, 487, 509, 563, 571, 607, 631, 647, 661, 727, 743, 757, 811, 863, 907, 907, 919, 977, 1031, 1051, 1061, 1117, 1181
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
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
|
|
|
LINKS
|
|
|
|
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
|
|
|
|
EXTENSIONS
|
|
|
|
STATUS
|
approved
|
| |
|
|
