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

1,1

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: A235165 A259505 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