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 A226752 Possible total sums of three 3-digit primes that together use all nonzero digits 1-9. 0
 999, 1089, 1107, 1197, 1269, 1287, 1323, 1341, 1359, 1377, 1413, 1431, 1449, 1467, 1521, 1539, 1557, 1593, 1611, 1629, 1647, 1683, 1701, 1737, 1773, 1791, 1809, 1827, 1863, 1881, 1899, 1917, 1953, 1971, 1989, 2007, 2043, 2061, 2133, 2151, 2223, 2241, 2331, 2421 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Split permutations of the digits 1 through 9 into three-digit parts, treat each part as a number, and total those numbers. The sequence contains all of the possible sums. REFERENCES David Wells, The Penguin Dictionary of Curious and Interesting Numbers (Rev. ed. 1997), p. 149 (entry for 999). LINKS Table of n, a(n) for n=1..44. EXAMPLE 149 + 263 + 587 = 999, and 149, 263, and 587 are all primes, so 999 is a (the smallest) term of the sequence. 653 + 827 + 941 = 2421, and 653, 827, and 941 are all primes, so 2421 is a (the largest) term of the sequence. MATHEMATICA Union[Transpose[Join[#, {Total[#]}]&/@(FromDigits/@Partition[#, 3]&/@ Select[Permutations[Range[9]], And@@PrimeQ[FromDigits/@ Partition[ #, 3]]&])][[4]]] PROG (Python) from sympy import isprime from itertools import permutations aset = set() for p in permutations("123456789"): p = [int("".join(p[i*3:(i+1)*3])) for i in range(3)] if all(isprime(pi) for pi in p): aset.add(sum(p)) print(sorted(aset)) # Michael S. Branicky, Jun 28 2021 CROSSREFS Cf. A226772 Sequence in context: A259505 A372046 A317594 * A043527 A117720 A110401 Adjacent sequences: A226749 A226750 A226751 * A226753 A226754 A226755 KEYWORD nonn,fini,full,base AUTHOR Harvey P. Dale, Jun 16 2013 EXTENSIONS Name clarified by Tanya Khovanova, Jul 05 2021 STATUS approved

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Last modified May 27 08:06 EDT 2024. Contains 372850 sequences. (Running on oeis4.)