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Search: id:A076787
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| A076787 |
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Pisumprimes: prime(k), where k is the sum of the first n digits of Pi. |
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+0
2
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| 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
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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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. - Frank Adams-Watters (FrankTAW(AT)Netscape.net), Mar 30 2006
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FORMULA
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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. In Maple prime(x) is ithprime(x).
a(n)=A000040(A046974(n)) - Frank Adams-Watters (FrankTAW(AT)Netscape.net), Mar 30 2006
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PROGRAM
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(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);
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CROSSREFS
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Sequence in context: A046078 A075409 A058079 this_sequence A094963 A045446 A106074
Adjacent sequences: A076784 A076785 A076786 this_sequence A076788 A076789 A076790
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KEYWORD
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easy,nonn,base
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AUTHOR
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Cino Hilliard (hillcino368(AT)gmail.com), Nov 16 2002
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EXTENSIONS
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Edited by T. D. Noe (noe(AT)sspectra.com), Jun 24 2009
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