A226752 Possible total sums of three 3-digit primes that together use all nonzero digits 1-9.

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

Offset: 1

Author

Harvey P. Dale, Jun 16 2013

Keywords

• nonn
• fini
• full
• base

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.

Examples

			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.
		

References

• David Wells, The Penguin Dictionary of Curious and Interesting Numbers (Rev. ed. 1997), p. 149 (entry for 999).

Crossrefs

Cf. A226772

Programs

Mathematica

Union[Transpose[Join[#,{Total[#]}]&/@(FromDigits/@Partition[#,3]&/@ Select[Permutations[Range[9]],And@@PrimeQ[FromDigits/@ Partition[ #,3]]&])][[4]]]

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

Extensions

Name clarified by Tanya Khovanova, Jul 05 2021