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A066888
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Number of primes p between triangular numbers T(n) < p <= T(n+1).
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10
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0, 2, 1, 1, 2, 2, 1, 2, 3, 2, 2, 3, 3, 3, 3, 2, 4, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 6, 4, 5, 3, 6, 6, 7, 5, 5, 6, 4, 8, 5, 6, 6, 8, 6, 8, 5, 7, 5, 11, 4, 6, 9, 7, 8, 9, 8, 7, 7, 9, 7, 8, 7, 12, 5, 9, 9, 11, 9, 7, 7, 12, 10, 10, 9, 9, 9, 6, 11, 10, 11, 9, 12, 11, 12, 9, 10, 11, 12, 10, 13, 9, 11, 10, 12
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| It is conjectured that for n > 0, a(n) > 0. See also A190661. [John W. Nicholson, May 18 2011]
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LINKS
| T. D. Noe, Table of n, a(n) for n = 1..10000
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FORMULA
| a(n) = pi(n*(n+1)/2)-pi(n*(n-1)/2).
a(n) equals the number of occurrences of n+1 in A057062. [Esko Ranta, Jul 29 2011]
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EXAMPLE
| Write the numbers 1, 2, ... in a triangle with n terms in the n-th row; a(n) = number of primes in n-th row.
Triangle begins
1 (0 primes)
2 3 (2 primes)
4 5 6 (1 prime)
7 8 9 10 (1 prime)
11 12 13 14 15 (2 primes)
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MATHEMATICA
| Table[PrimePi[(n^2 + n)/2] - PrimePi[(n^2 - n)/2], {n, 96}] (* From Alonso del Arte, Sep 03 2011 *)
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PROG
| (PARI) { tp(m)=local(r, t); r=1; for(n=1, m, t=0; for(k=r, n+r-1, if(isprime(k), t++)); print1(t", "); r=n+r; ) }
(PARI) {tpf(m)=local(r, t); r=1; for(n=1, m, t=0; for(k=r, n+r-1, if(isprime(k), t++); print1(k" ")); print1(" ("t" prime)"); print(); r=n+r; ) }
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CROSSREFS
| Cf. A083382.
Essentially the same as A065382 and A090970.
Cf. A000217, A000040, A014085, A190661.
Sequence in context: A109705 A025848 A065382 * A029313 A144001 A124233
Adjacent sequences: A066885 A066886 A066887 * A066889 A066890 A066891
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Jun 06 2003
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EXTENSIONS
| More terms from Vladeta Jovovic (vladeta(AT)eunet.rs) and Jason Earls (zevi_35711(AT)yahoo.com), Jun 06 2003
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