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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 (list; graph; refs; listen; history; text; internal format)
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;
end do: # R. J. Mathar, Jul 12 2013
CROSSREFS
Sequence in context: A200723 A135738 A307574 * A073851 A290541 A043321
KEYWORD
nonn,base
AUTHOR
STATUS
approved

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Last modified April 24 04:14 EDT 2024. Contains 371918 sequences. (Running on oeis4.)