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

1,1

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

Links

Table of n, a(n) for n=1..22.

Peter Luschny, Strong coprimality, November 2010.

Robert Munafo, Low bases with many divisibility tests

Formula

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

Example

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")

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

Crossrefs

Cf. A001221, A181834.

Sequence in context: A059842 A001529 A363505 * A116632 A214343 A007364

Adjacent sequences: A069351 A069352 A069353 * A069355 A069356 A069357

Keyword

nonn,more

Author

Robert Munafo, Nov 19 2002

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

Status

approved