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

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

Offset: 1

Author

Cino Hilliard, Nov 16 2002

Keywords

• easy
• nonn
• base

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

Programs

Mathematica

Prime[#]&/@Accumulate[RealDigits[Pi,10,40][[1]]] (* Harvey P. Dale, Sep 30 2012 *)

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); }

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.

a(n)=A000040(A046974(n)) - Franklin T. Adams-Watters, Mar 30 2006

Extensions

Edited by T. D. Noe, Jun 24 2009