A108638 Semiprime plus its digits is semiprime.

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

Author

Zak Seidov, Jun 14 2005

Keywords

• nonn
• base

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

Examples

			15=3*5 and 15+1+5=21=3*7.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001358, A062028, A066568.

Programs

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&]