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Search: id:A082676
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| A082676 |
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Constant term of polynomial of degree n passing through the first n+1 consecutive prime-index-primes. |
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+0
1
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| 1, 5, 9, 21, 53, 129, 303, 695, 1543, 3251, 6375, 11411, 18113, 23877, 20517, -11385, -111285, -350599, -844759, -1752605, -3220485, -5146003, -6428481, -2891081, 17977615, 89400059, 292685805, 814545349, 2061282923, 4876315217, 10937900039, 23459793869, 48384441535, 96352980717
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Eventually some terms will be negative.
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FORMULA
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Prime-index-primes (PIPS) are generated by prime(prime(x)) x=1, 2...
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EXAMPLE
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For n = 3, the polynomial p(x) = (-2/3)x^3 + 6x^2 - (34/3)x + 9 satisfies p(1) = 3, p(2) = 5, p(3) = 11, and p(4) = 17, so a(3) = 9.
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PROGRAM
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(PARI) for (i = 2, 50, x = vector(i); y = x; for (j = 1, i, y[j] = prime(prime(j)); x[j] = j); q = polinterpolate(x, y, 0); print(q))
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CROSSREFS
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Sequence in context: A083943 A097074 A050559 this_sequence A110200 A063404 A102177
Adjacent sequences: A082673 A082674 A082675 this_sequence A082677 A082678 A082679
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KEYWORD
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easy,sign
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AUTHOR
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Cino Hilliard (hillcino368(AT)gmail.com), May 19 2003
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EXTENSIONS
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More terms from David Wasserman (wasserma(AT)spawar.navy.mil), Sep 23 2004
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