1,1

This sequence is of use in non-decimal systems whereby digits in base a(n) can be tested using simple addition tricks [and no higher operations] to determine if the number represented is relatively prime with respect to the first n primes.

The addition trick for base a(n) is to sum digits to do a(n)-1 divisibility tests and alternately add and subtract digits to perform the a(n)+1 test. In base 10 we add digits to find 9-divisibility or add-subtract digits (e.g. 132 = 2-3+1 = 0 is divisible by 11) to find divisibility by 11.

a(5) = 21 because 20, 21 and 22 have between them all 5 prime factors 2,3,5,7,11. - Don Reble (djr(AT)nk.ca), Feb 27 2003

Jeffrey C. Jacobs, Time Horse Home.

Robert Munafo, Interesting Numbers.

a(n) is the smallest number such that the product [a(n)-1]a(n)[a(n)+1] has prime factors which include the first n ordinal primes excluding 1 (see A033946).

a(1) = 1 since we assume 0 and 1 have no nontrivial prime factors, thus a(1)+1 is the only term with factors, {2}.

a(4) = 6 because a(4)-1 = 5, thus the set of prime factors {5}; a(4) = 2*3, thus the set of prime factors {2, 3} and a(4)+1 = 7 with the set of prime factors {7}. The combined set, {2, 3, 5, 7} contains the first 4 prime numbers (not including 1) and because there are no numbers less than 6 with this property, a(4) = 6.

a = 1 firstNPrimes = getFirstNPrimes(n) /* A033946[1:n+1] */ a = 0 do { ++a; primes = prime_factors(a) primes.union(prime_factors(a-1)) primes.union(prime_factors(a+1)) } while (!(firstNPrimes is_subset_of primes)) return a;

Cf. A033946.

Sequence in context: A153961 A134041 A069925 this_sequence A072707 A086105 A084701

Adjacent sequences: A080608 A080609 A080610 this_sequence A080612 A080613 A080614

nonn

Jeffrey C. Jacobs (darklord(AT)timehorse.com), Feb 26 2003

More terms from Don Reble (djr(AT)nk.ca), Feb 27 2003