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A108638
Semiprime plus its digits is semiprime.
2
15, 22, 26, 33, 38, 39, 49, 51, 55, 57, 74, 77, 115, 123, 129, 134, 145, 155, 161, 169, 178, 187, 202, 206, 213, 214, 221, 237, 254, 265, 274, 278, 291, 299, 301, 303, 309, 321, 327, 335, 361, 371, 377, 381, 382, 386, 411, 437, 445, 466, 478, 485, 497, 505
OFFSET
1,1
COMMENTS
Members k of A001358 such that A062028(k) is in A001358. - Robert Israel, Oct 01 2024
Surprisingly there are only three(?) semiprimes sp, 10,14,15, such that sp minus its digits is semiprime.
That is because n - (sum of its digits) = A066568(n) is divisible by 9. - Robert Israel, Oct 01 2024
LINKS
EXAMPLE
15=3*5 and 15+1+5=21=3*7.
MAPLE
filter:= n -> numtheory:-bigomega(n) = 2 and numtheory:-bigomega(n+convert(convert(n, base, 10), `+`))=2:
select(filter, [$1..1000]); # Robert Israel, Oct 01 2024
MATHEMATICA
Select[Range[500], Plus@@Last/@FactorInteger[ # ]==Plus@@Last/@FactorInteger[ #+Plus@@IntegerDigits[ # ]]==2&]
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Zak Seidov, Jun 14 2005
STATUS
approved