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Search: A147517
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| A147517 |
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Number of pairs of primes p<q such that (p+q)/2=A002110(n), the n-th primorial. |
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+30
2
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OFFSET
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1,3
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COMMENT
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The sequence is infinite and illustrates the number of primes expected to be centered around a given primorial.
Given ever increasing primorial P, one can expect to find the highest symmetrical prime just below 2P.
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FORMULA
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Using a limited dataset, the approximate relation is the quadratic Y=Ax^2+Bx+C (A,B,C)=(0.12267, 0.75758, -1.592)
where Y= Ln(# prime pairs) (each > the prime factors) and x is # prime factors of the seed primorial.
Thus the number of pairs ~ Exp[Y]. For example, the fit yields EXP(7.370)=1587 prime pairs for pf=6 (30030) while actual=1564. Gnumeric spreadsheet was used for data analysis.
a(n)=A002375(A002110(n)) [From T. D. Noe (noe(AT)sspectra.com), Nov 07 2008]
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EXAMPLE
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There are 6 pairs centered at primorial=30: (29,31),(23,37),(19,41),(17,43),(13,47),(7,53)
As they are symmetrical, each prime pair sums to twice the primorial center.
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PROGRAM
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(PARI) The values were computed with custom PariGP script using its ispseudoprime test. Here is the script link: http://billymac00.pbwiki.com/f/mirrors.gp
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CROSSREFS
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Inputs from A002110
Sequence in context: A063888 A029571 A109501 this_sequence A005922 A057896 A147779
Adjacent sequences: A147514 A147515 A147516 this_sequence A147518 A147519 A147520
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KEYWORD
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easy,more,nonn
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AUTHOR
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Bill R McEachen (bmceachen(AT)centralsan.org), Nov 05 2008
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EXTENSIONS
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Better description by T. D. Noe (noe(AT)sspectra.com), Nov 09 2008
Corrected typo. - T. D. Noe (noe(AT)sspectra.com), Nov 10 2008
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| A147853 |
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Least prime p such that there is a prime q with (p+q)/2=A002110(n), the n-th primorial. |
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+10
1
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| 5, 7, 11, 17, 19, 19, 29, 37, 37, 37, 73, 47, 59, 71, 97, 79, 79, 101, 97, 137, 227, 137, 109, 127, 151, 127, 151, 151, 179, 227, 431, 139, 211, 223, 337, 181, 251, 257, 313, 227, 257, 227, 263, 491, 307, 241, 409, 263, 277
(list; graph; listen)
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OFFSET
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2,1
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COMMENT
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Improved description from T. D. Noe (noe(AT)sspectra.com).
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EXAMPLE
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For primorial=30, (p,q)=(7,53) as 7+53=2*30
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PROGRAM
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(PARI) ospp(N)= { i=4; while(1, Q=2*N-prime(i); if( ispseudoprime(2*N-prime(i)), print(N, ", ", prime(i) ); return(1) ); i++ ); \end WHILE }
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CROSSREFS
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Cf. A002110, A147517
Sequence in context: A072055 A164316 A107448 this_sequence A111226 A168224 A084197
Adjacent sequences: A147850 A147851 A147852 this_sequence A147854 A147855 A147856
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KEYWORD
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easy,nonn
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AUTHOR
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Bill R McEachen (bmceache(AT)centralsan.org), Nov 15 2008
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