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Search: id:A088973
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| A088973 |
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Number of twin prime pairs between consecutive prime index primes of order 4. The bounds are included in the calculation. |
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1
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| 5, 20, 26, 76, 51, 93, 61, 100, 176, 122, 207, 156, 90, 152, 249, 280, 44, 412, 178, 91, 293, 270, 282, 374, 340, 158, 186, 121, 169, 913, 263, 235, 255, 597, 162, 406, 457, 263, 418, 339, 221, 645, 161, 300, 134, 855, 1235, 236, 162, 241, 256, 243, 786, 261
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Conjecture: PIPS4(x) -> PIPS4(x+1) always contains 1 or more twin prime pairs. Proof of this would be proof of an infinity of twin primes.
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FORMULA
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PIPS4(x)= Prime-index-primes of order 4 = prime(prime(prime(prime(prime(x))))) where prime(x) is the xth prime. Seq = count of twins in PIPS4(x) -> PIPS(x+1).
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PROGRAM
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(PARI) piptwins4(m, n) = { for(x=m, n, f=1; c=0; p1 = prime(prime(prime(prime(prime(x))))); p2 = prime(prime(prime(prime(prime(x+1))))); forprime(j=p1, p2, if(isprime(j+2), f=0; c++) ); print1(c", "); ) }
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CROSSREFS
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Sequence in context: A101728 A053240 A034123 this_sequence A005240 A080654 A074219
Adjacent sequences: A088970 A088971 A088972 this_sequence A088974 A088975 A088976
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KEYWORD
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nonn,uned
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AUTHOR
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Cino Hilliard (hillcino368(AT)gmail.com), Oct 30 2003
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