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 A299732 a(n) has exactly (a(n) - n) / 2 partitions with exactly (a(n) - n) / 2 prime parts. 2
 2, 5, 8, 13, 20, 29, 42, 57, 78, 109, 148, 197, 264, 347, 454, 595, 770, 989, 1272, 1619, 2054, 2601, 3268, 4087, 5108, 6347, 7860, 9713, 11948, 14653, 17944, 21881, 26614, 32311, 39102, 47211, 56910, 68397, 82038, 98237, 117354, 139923, 166580, 197877, 234672 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS If B={b(n)} is the complement of A299731 then no number exists that has exactly b(n) partitions that have exactly b(n) prime parts, so this sequence lists only those numbers that can have the equality property. Up to a(44) = 234672 (currently, the last term), except for 2,5,8, and 29, every term is the sum of distinct previous terms. Will this be true for all new terms? LINKS J. Stauduhar, Python program. FORMULA a(n) = 2*A299731(n) + n = 2*A222656(3*n,n) + n. EXAMPLE For n = 3: A299731(3) = 5. a(3) = 2*5 + 3 = 13. The five partitions of 13 that have exactly five prime parts are: (5,2,2,2,2), (3,3,3,2,2), (3,3,2,2,2,1), (3,2,2,2,2,1,1), and (2,2,2,2,2,1,1,1), so a(3) = 13. PROG (PYTHON) See Stauduhar link. CROSSREFS Cf. A222656, A299730, A299731. Sequence in context: A054254 A025216 A076059 * A169952 A025279 A169954 Adjacent sequences:  A299729 A299730 A299731 * A299733 A299734 A299735 KEYWORD nonn AUTHOR J. Stauduhar, Feb 18 2018 STATUS approved

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Last modified September 22 10:34 EDT 2020. Contains 337289 sequences. (Running on oeis4.)