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 A090919 Primes arising as the arithmetic mean of first n terms of A090918. 2
 3, 5, 7, 11, 17, 23, 31, 43, 73, 101, 131, 157, 191, 239, 293, 379, 571, 757, 937, 1123, 1301, 1481, 1697, 1907, 2113, 2371, 2617, 2857, 3121, 3389, 3709, 4021, 4337, 4637, 4937, 5227, 5503, 5779, 6047, 6311, 6569, 6829, 7079, 7349, 7639, 7927, 8263, 8599 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS a(1000) = 13918649. - Rick L. Shepherd, Mar 08 2004 Intersection of A090918 and A090919: 3,7,11,23,11161,4197541. - Zak Seidov, Apr 05 2011. Contribution by Vladimir Shevelev, Nov 24 2012 (Start) A recursive algorithm of parallel calculation of A090918 and A090919. Together with a(n)=A090919(n), denote b(n)=A090918(n). We begin with a(1)=b(1)=3; if, for n>=2, we know a(n-1) and b(n-1), then a(n) is the smallest prime x such that n*x-(n-1)*a(n-1) is a prime greater than b(n-1). Now, knowing a(n), we have b(n) = n*a(n) - (n-1)*a(n-1). For example, suppose that we know that a(5)=17, b(5)=41. To find a(6) and b(6), consider inequality 6*x - 5*17 > 41, where x is prime. Thus we consider x >= 23. Since, already for x=23, 6*x-5*17=53 is prime, then a(6)=23, b(6)=53. (End) LINKS Zak Seidov, Table n, a(n) for n=1..2000 MATHEMATICA f[s_] := Block[{m = 1 + Length@ s, p = NextPrime@ s[[-1]], ss = Plus @@ s}, While[ !PrimeQ[(ss + p)/m], p = NextPrime@ p]; Append[s, p]]; s = Nest[f, {3}, 41]; (Accumulate@ s)/Range@ 42 (* Robert G. Wilson v, Dec 15 2012 *) PROG (PARI) {terms=100; A090918=A090919=vector(terms); A090918[1]=A090919[1]=3; s=0; for(k=2, terms, s=s+A090918[k-1]; p=A090918[k-1]+1; until(isprime(p) && (denominator((s+p)/k)==1) && isprime((s+p)/k), p++); A090918[k]=p; A090919[k]=(s+p)/k; print1(A090919[k], ", ") ); A090919} CROSSREFS Cf. A090940, A090941, A090918. Sequence in context: A108539 A170886 A238137 * A065557 A266164 A152999 Adjacent sequences: A090916 A090917 A090918 * A090920 A090921 A090922 KEYWORD nonn AUTHOR Amarnath Murthy, Dec 16 2003 EXTENSIONS Corrected and extended by Rick L. Shepherd, Mar 08 2004 STATUS approved

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Last modified March 22 12:10 EDT 2023. Contains 361423 sequences. (Running on oeis4.)