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

2, 3, 6, 15, 66, 210, 715, 7315, 38571, 254541, 728365, 11243155, 58524466, 812646121, 5163068911, 58720148851, 555409903686, 4339149420606, 69322940121436, 490005293940085, 5819629108725510, 76622240600506315

Offset: 1

Author

Robert Munafo, Nov 19 2002

Keywords

• nonn
• more

Comments

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

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

10^13 < a(19) <= 69322940121436. - Giovanni Resta, Mar 24 2020

Examples

			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")
		

Links

• Peter Luschny, Strong coprimality, November 2010.
• Robert Munafo, Low bases with many divisibility tests

Crossrefs

Cf. A001221, A181834.

Programs

Maple

A069354_list := proc(n) local i, L, Max; Max := 1; L := NULL;
for i from 2 to n do
   if nops(numtheory[factorset](i*(i-1))) = Max
   then Max := Max + 1; L := L,i fi;
od;
L end:  # Peter Luschny, Nov 12 2010

Formula

a(n) = A059958(n) + 1 for 0 < n < 19. - Robert G. Wilson v, Feb 18 2014

Extensions

More terms added using data from A059958 (see there for credits) by M. F. Hasler, Jan 15 2014

a(19)-a(21) from Michael S. Branicky, Feb 11 2023

a(22) from Michael S. Branicky, Feb 23 2023