

A169911


Primes in carryless digital root arithmetic in base 10.


4



3, 6, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 31, 32, 34, 35, 37, 38, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 61, 62, 64, 65, 67, 68, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87
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OFFSET

1,1


COMMENTS

Addition and multiplication are the same as in school, that is, done in base 10, except that there are no carries and when individual digits are added or multiplied the result is replaced by its digital root (A010888).
The units are {1,2,4,5,7,8}. A prime is a number N whose only factorizations are of the form N = u*M where u is a unit.
All numbers of the form 100...01 (with k >= 0 zeros) are prime, so there are infinitely many primes.


LINKS



EXAMPLE

96 has a representation 31*6 and is not in the sequence.


MAPLE

# carryLmult implemented in A169908
isA169911 := proc(n)
local a, b, un ;
un := {1, 2, 4, 5, 7, 8} ;
for a from 1 to n do
for b from 1 to a do
if a in un or b in un then
;
else
if carryLmult(a, b) = n then
return false;
end if;
end if;
end do:
end do:
if n in un then
false ;
else
true;
end if;
end proc:
e := 1:
for n from 1 do
if isA169911(n) then
printf("%d %d\n", e, n) ;
e := e+1 ;
end if;


CROSSREFS



KEYWORD

nonn,base


AUTHOR



STATUS

approved



