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A069354 Lowest base with simple divisibility test for n primes; smallest B such that omega(B) + omega(B-1) = n.

%I A069354 #41 Feb 23 2023 19:20:22
%S A069354 2,3,6,15,66,210,715,7315,38571,254541,728365,11243155,58524466,
%T A069354 812646121,5163068911,58720148851,555409903686,4339149420606,
%U A069354 69322940121436,490005293940085,5819629108725510,76622240600506315
%N A069354 Lowest base with simple divisibility test for n primes; smallest B such that omega(B) + omega(B-1) = n.
%C A069354 Indices of record values of primepi(n) - A181834(n) (the number of primes <= n which are not strongly prime to n). - _Peter Luschny_, Mar 17 2013
%C A069354 As pointed out by _Don Reble_ on the SeqFan list, one has a(n) = A059958(n)+1 at least up to a(18), since so far A001221(m*(m+1)) = n (and not ">") for m = A059958(n). - _M. F. Hasler_, Jan 15 2014
%C A069354 10^13 < a(19) <= 69322940121436. - _Giovanni Resta_, Mar 24 2020
%H A069354 Peter Luschny, <a href="http://oeis.org/wiki/User:Peter_Luschny/StrongCoprimality">Strong coprimality</a>, November 2010.
%H A069354 Robert Munafo, <a href="http://www.mrob.com/pub/math/seq-a069354.html">Low bases with many divisibility tests</a>
%F A069354 a(n) = A059958(n) + 1 for 0 < n < 19. - _Robert G. Wilson v_, Feb 18 2014
%e A069354 a(4) = 15 because in base 15 you can test for divisibility by 4 different primes (3 and 5 directly, 2 and 7 by "casting out 14's")
%p A069354 A069354_list := proc(n) local i, L, Max; Max := 1; L := NULL;
%p A069354 for i from 2 to n do
%p A069354    if nops(numtheory[factorset](i*(i-1))) = Max
%p A069354    then Max := Max + 1; L := L,i fi;
%p A069354 od;
%p A069354 L end:  # _Peter Luschny_, Nov 12 2010
%Y A069354 Cf. A001221, A181834.
%K A069354 nonn,more
%O A069354 1,1
%A A069354 _Robert Munafo_, Nov 19 2002
%E A069354 More terms added using data from A059958 (see there for credits) by _M. F. Hasler_, Jan 15 2014
%E A069354 a(19)-a(21) from _Michael S. Branicky_, Feb 11 2023
%E A069354 a(22) from _Michael S. Branicky_, Feb 23 2023