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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 N. J. A. Sloane, Table of n, a(n) for n = 1..458 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 Adjacent sequences:  A169908 A169909 A169910 * A169912 A169913 A169914 KEYWORD nonn,base AUTHOR David Applegate, Marc LeBrun and N. J. A. Sloane, Jul 11 2010 STATUS approved

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Last modified January 19 06:28 EST 2021. Contains 340266 sequences. (Running on oeis4.)