cp's OEIS Frontend

A076787 Pisumprimes: prime(k), where k is the sum of the first n digits of Pi.

%I A076787 #15 May 25 2018 08:27:05
%S A076787 5,7,19,23,43,83,97,127,151,167,193,239,283,337,389,409,421,439,487,
%T A076787 509,563,571,607,631,647,661,727,743,757,811,863,907,907,919,977,1031,
%U A076787 1051,1061,1117,1181
%N A076787 Pisumprimes: prime(k), where k is the sum of the first n digits of Pi.
%C A076787 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
%F A076787 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.
%F A076787 a(n)=A000040(A046974(n)) - _Franklin T. Adams-Watters_, Mar 30 2006
%t A076787 Prime[#]&/@Accumulate[RealDigits[Pi,10,40][[1]]] (* _Harvey P. Dale_, Sep 30 2012 *)
%o A076787 (PARI) \\ pi digit sum index primes; pisump.gp Primes whose index is the sequential sum of digits of pi
%o A076787 { 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); }
%K A076787 easy,nonn,base
%O A076787 1,1
%A A076787 _Cino Hilliard_, Nov 16 2002
%E A076787 Edited by _T. D. Noe_, Jun 24 2009