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

1,1

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

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

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

Cf. A001358, A062028, A066568.

Sequence in context: A018888 A115174 A092783 * A076379 A227095 A038753

Adjacent sequences: A108635 A108636 A108637 * A108639 A108640 A108641

Keyword

nonn,base

Author

Zak Seidov, Jun 14 2005

Status

approved