

A090970


Number of primes strictly between T(n) and T(n+1), where T(n) = nth triangular number.


4



1, 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
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OFFSET

1,4


LINKS

T. D. Noe, Table of n, a(n) for n = 1..10000


EXAMPLE

a(8)=3 because between T(8)=36 and T(9)=45 we have the prime numbers 37,41 and 43.


MAPLE

a:= proc(n) local ct, j: ct:=0: for j from n*(n+1)/2+1 to (n+1)*(n+2)/21 do if isprime(j)=true then ct:=ct+1 else ct:=ct fi: od: end: seq(a(n), n=1..103); # Emeric Deutsch, Feb 23 2005


MATHEMATICA

With[{trs=Partition[Accumulate[Range[100]], 2, 1]}, Join[{1}, Rest[ PrimePi[ #[[2]]] PrimePi[#[[1]]]&/@trs]]] (* Harvey P. Dale, Aug 25 2015 *)


CROSSREFS

Essentially the same as A065382 and A066888.
Sequence in context: A238325 A238885 A023566 * A091972 A025833 A200647
Adjacent sequences: A090967 A090968 A090969 * A090971 A090972 A090973


KEYWORD

nonn


AUTHOR

Amarnath Murthy, Jan 03 2004


EXTENSIONS

More terms from Emeric Deutsch, Feb 23 2005


STATUS

approved



