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Search: id:A078445
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| A078445 |
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Primes in A060620, i.e. primes which are integer parts of averages of initial primes. |
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+0
3
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| 2, 2, 3, 5, 11, 23, 29, 31, 53, 67, 79, 89, 97, 107, 149, 163, 223, 229, 241, 271, 277, 283, 307, 313, 347, 353, 373, 379, 401, 433, 443, 449, 479, 521, 541, 547, 557, 571, 601, 631, 659, 673, 683, 769, 797, 811, 821, 839, 853, 857, 881, 907, 953, 971, 1033, 1051
(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 the averages and integer parts of the averages both appear to converge. The difference between the two converges to 0.15971929...
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FORMULA
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Seq(n) = Floor((Sum(prime(x), x=1..k)/k) where k = 1, 2... prime(k) <= n
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EXAMPLE
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11 is in the sequence since average of first 10 primes is [(2+3+5+7+11+13+17+19+23+29)/10] = [119/10] = 11.
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PROGRAM
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(PARI) \ moving average of the primes movavgp(p) = { ct=s=sr1=sr2=0; forprime(x=2, p, ct++; s+=x; y = floor(s/ct +.0); if(isprime(y), sr1+=1.0/y; sr2+=1.0/(s/ct); print1(y" "); ); ); print(); print(sr1" "sr2); print(); print(sr1-sr2); }
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CROSSREFS
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Cf. A060620.
Sequence in context: A058697 A030427 A049907 this_sequence A127166 A005426 A014644
Adjacent sequences: A078442 A078443 A078444 this_sequence A078446 A078447 A078448
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KEYWORD
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easy,nonn
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AUTHOR
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Cino Hilliard (hillcino368(AT)gmail.com), Dec 31 2002
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EXTENSIONS
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Edited by Henry Bottomley (se16(AT)btinternet.com), Jan 02 2003
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