

A226752


Possible total sums of three 3digit primes that together use all nonzero digits 19.


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
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OFFSET

1,1


COMMENTS

Split permutations of the digits 1 through 9 into threedigit 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



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))


CROSSREFS



KEYWORD

nonn,fini,full,base


AUTHOR



EXTENSIONS



STATUS

approved



