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 A090970 Number of primes strictly between T(n) and T(n+1), where T(n) = n-th 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 (list; graph; refs; listen; history; text; internal format)
 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)/2-1 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

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Last modified August 24 18:12 EDT 2019. Contains 326295 sequences. (Running on oeis4.)