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A242045 Numbers that can be written as a sum of prime numbers, where all of the digits from 1 to 5 appear exactly once in the primes. 0
51, 69, 96, 249, 294, 429, 438, 474, 546, 564, 1428, 1455, 1545, 2148, 2346, 3543, 4155, 4236, 4515, 5415, 5433 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Only two numbers have more than one solution, 294, which has two:

294 = 43 + 251,

294 = 53 + 241.

And 564, which has three:

564 = 23 + 541,

564 = 41 + 523,

564 = 43 + 521.

Also, permutations of numbers are extremely common. 69 and 96; 249,294 and 429; 546 and 564; 1428 and 2148; 1455, 1545, 4155, 4515 and 5415; 2346 and 4236; 3543 and 5433. In fact, there are only 3 numbers from a total of 21 that do not have any permutations associated with it. These are 51, 438 and 474.

Another odd fact: the sum of the digits of every single value, except 51, is 15. (note: not actually odd. Since 1 + 2 + 3 + 4 + 5 = 15 and digitSum (a + b) = digitSum( digitSum(a) + digitSum(b) ))

LINKS

Table of n, a(n) for n=1..21.

EXAMPLE

51 = 2 + 3 + 5 + 41.

69 = 5 + 23 + 41.

96 = 2 + 41 + 53.

CROSSREFS

Sequence in context: A015863 A232105 A225801 * A113285 A050698 A039474

Adjacent sequences:  A242042 A242043 A242044 * A242046 A242047 A242048

KEYWORD

nonn,base,fini,full

AUTHOR

Raffa Freitas, Aug 12 2014

STATUS

approved

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Last modified December 8 08:31 EST 2021. Contains 349594 sequences. (Running on oeis4.)