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 A240301 a(n) is the number of sets of three positive integers p_1 < p_2 < p_3 such that 2*p_2 = p_1 + p_3, where p_i (i=1,2,3) is either 1 or a prime number and p_3 = prime(n). 1
 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 1, 2, 3, 1, 3, 3, 2, 2, 4, 3, 4, 4, 4, 2, 3, 4, 3, 3, 5, 5, 5, 4, 5, 4, 5, 4, 5, 5, 6, 4, 4, 7, 4, 6, 7, 6, 7, 5, 4, 5, 4, 6, 8, 7, 7, 7, 7, 4, 8, 9, 8, 5, 9, 6, 7, 8, 4, 8, 8, 10, 8, 6, 6, 10, 9, 9, 7, 7, 6, 9, 10, 9, 8, 8, 12, 13 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,7 COMMENTS a(n)>0 for n > 1. It is conjectured that every positive integer appears a positive finite number of times in this sequence. The sequence of records is 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 16, 18, 20, 21, 22, 23, 24, 25, 27, 28, 31, 33, 34, 35, 36, 39, 40, 41, 42, 43, 46, 47, 48, 50, 51, 53, 55, 56, 58, 61, 62, 64, 65, 66, 70, 71, 72, 74, 76, 78,... - R. J. Mathar, May 02 2014 Alternative definition for p_i is p_1 is either 1 or an odd prime, p_2 is an odd prime after a(2) and p_3 is prime(n). - Jon Perry, Apr 17 2014. LINKS Lei Zhou, Table of n, a(n) for n = 2..10001 EXAMPLE For n=2, p_3=prime(2)=3, 2*2=1+3. One instance found, so a(2)=1; ... For n=8, p_3=prime(8)=19, 2*11=3+19, 2*13=7+19. Two instances found, so a(8)=2; ... For n=30, p_3=prime(30)=113, 2*59=5+113, 2*71=29+113, 2*83=53+113, 2*101=89+113, 2*107=101+113. Five instances found, so a(30)=5. MATHEMATICA Table[p = Prime[n]; ct = 0; pp = p; While[pp = NextPrime[pp, -1]; diff = p - pp; diff < pp, cp = pp - diff; If[(PrimeQ[cp]) || (cp == 1), ct++]]; ct, {n, 2, 87}] CROSSREFS Cf. A000040, A240232. Sequence in context: A052435 A094701 A210452 * A289641 A209312 A054715 Adjacent sequences:  A240298 A240299 A240300 * A240302 A240303 A240304 KEYWORD nonn,easy AUTHOR Lei Zhou, Apr 03 2014 STATUS approved

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Last modified August 20 10:03 EDT 2019. Contains 326144 sequences. (Running on oeis4.)