A076789 Phisumprimes: prime(k), where k is the sum of the first n digits of phi-1 and phi is the golden ratio.
13, 17, 47, 47, 61, 73, 113, 163, 199, 241, 269, 317, 373, 431, 449, 499, 523, 587, 599, 599, 617, 647, 701, 743, 809, 823, 853, 863, 911, 947, 991, 1013, 1061, 1063, 1069, 1117, 1181, 1193, 1193, 1217, 1217, 1283, 1289, 1321, 1427, 1471, 1471, 1493, 1553
Offset: 1
Crossrefs
Cf. A076787, which is the same algorithm for the digits of Pi.
Programs
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Mathematica
Prime[#]&/@Accumulate[RealDigits[GoldenRatio-1,10,50][[1]]] (* Harvey P. Dale, Sep 30 2012 *)
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PARI
\\ phi digit sum index primes; phisump.gp Primes whose index is the sequential sum of digits of phi { phisump(n) = default(realprecision, 100000); p = (sqrt(5)-1)/2; 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 Phi = (sqrt(5)-1)/2 are added (d_1 + d_2 + ... + d_i) and the prime whose index is the i-th sum is chosen. E.g., for Phi = .618033989... the first Phisumprime is prime(6) the second is prime(7), 3rd is prime(15), etc. Let d_1, d_2, ..., d_i be the expansion of the decimal digits of Phi. Then Phisumprime(n)= prime(d_1), prime(d_1+d_2), ..., prime(Sum_{i=1..n} d_i). This can be generalized to Phisumprime(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)); for z=3 prime (prime(prime(x))); etc.
Extensions
Edited by T. D. Noe, Jun 24 2009
Comments