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A076789 Phisumprimes: prime(k), where k is the sum of the first n digits of phi-1 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 (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. Note that this is based on phi - 1, not phi. - Franklin T. Adams-Watters, 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 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.

a(n) = A000040(A093083(n+1)-1). - Franklin T. Adams-Watters, Mar 30 2006

MATHEMATICA

Prime[#]&/@Accumulate[RealDigits[GoldenRatio-1, 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

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Last modified October 17 13:57 EDT 2019. Contains 328113 sequences. (Running on oeis4.)