A073898 a(1) = 1; for n>1, a(n) = smallest even or odd number not occurring earlier accordingly as n is prime or composite.
1, 2, 4, 3, 6, 5, 8, 7, 9, 11, 10, 13, 12, 15, 17, 19, 14, 21, 16, 23, 25, 27, 18, 29, 31, 33, 35, 37, 20, 39, 22, 41, 43, 45, 47, 49, 24, 51, 53, 55, 26, 57, 28, 59, 61, 63, 30, 65, 67, 69, 71, 73, 32, 75, 77, 79, 81, 83, 34, 85, 36, 87, 89, 91, 93, 95, 38, 97, 99, 101, 40, 103
Offset: 1
Programs
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Maple
A073898 :=proc(nmax) local a,n,k; a := [1] ; while nops(a) < nmax do n := nops(a)+1 ; if isprime(n) then k :=2; else k :=1; fi ; while k in a do k := k+2 ; od ; a := [op(a),k] ; od ; RETURN(a) ; end: op(A073898(80)) ; # R. J. Mathar, Jun 27 2007
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Mathematica
Table[(4 PrimePi[n] - 2 n - 1)*(PrimePi[n] - PrimePi[n - 1]) + 2 (n - PrimePi[n - 1]) - 1, {n, 72}] (* Michael De Vlieger, Nov 11 2015 *) -
PARI
vector(100, n, (4*primepi(n)-2*n-1)*(primepi(n)-primepi(n-1))+2*(n-primepi(n-1))-1) \\ Altug Alkan, Oct 29 2015
Formula
a(n) = (4*pi(n)-2*n-1)*(pi(n)-pi(n-1)) + 2*(n - pi(n-1)) - 1, where pi = A000720. - Robert Israel, Oct 28 2015
Extensions
Corrected and extended by R. J. Mathar, Jun 27 2007
Comments