

A076789


Phisumprimes: prime(k), where k is the sum of the first n digits of phi1 and phi is the golden ratio.


1



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
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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. Note that this is based on phi  1, not phi.  Franklin T. AdamsWatters, Mar 30 2006


LINKS

Table of n, a(n) for n=1..49.


FORMULA

The digits of Phi = (sqrt(5)1)/2 are added (d_1 + d_2 + ... + d_i) and the prime whose index is the ith 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.
a(n) = A000040(A093083(n+1)1).  Franklin T. AdamsWatters, Mar 30 2006


MATHEMATICA

Prime[#]&/@Accumulate[RealDigits[GoldenRatio1, 10, 50][[1]]] (* Harvey P. Dale, Sep 30 2012 *)


PROG

(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);


CROSSREFS

Cf. A076787, which is the same algorithm for the digits of Pi.
Sequence in context: A248474 A140533 A180527 * A089577 A214393 A060569
Adjacent sequences: A076786 A076787 A076788 * A076790 A076791 A076792


KEYWORD

easy,nonn,base


AUTHOR

Cino Hilliard, Nov 16 2002


EXTENSIONS

Edited by T. D. Noe, Jun 24 2009


STATUS

approved



