A242298 Once a number in this sequence is divisible by all numbers 1 to m, subsequent terms are constrained to have the same property; choose the smallest permissible number that is greater than the previous term.

1, 2, 4, 6, 12, 24, 36, 48, 60, 120, 180, 240, 300, 360, 420, 840, 1680, 2520, 5040, 7560, 10080, 12600, 15120, 17640, 20160, 22680, 25200, 27720, 55440, 83160, 110880, 138600, 166320, 194040, 221760, 249480, 277200, 304920, 332640, 360360, 720720, 1441440

Offset

1,2

Comments

All terms from A095848 belong to this sequence.

Links

David A. Corneth, Table of n, a(n) for n = 1..10000

Formula

a(1) = 1. If n > 1, a(n) = a(n-1) + A368777(a(n-1)). - Hal M. Switkay, Jan 26 2024

Example

After 6, none of 7,8,9,10 or 11 are in the sequence since they are not divisible by 1,2 and 3 as 6 is. 12 is a term, but is now divisible by 1,2,3 and 4, adding a new constraint on subsequent terms.
After 24, 30 is not in the sequence because 24 is divisible by all numbers from 1 to 4 and 30 is not divisible by 4. But 36, which is divisible by all of 1 through 4, is a term.
As an irregular table, the n-th row consists of all numbers divisible by A051451(n) but not by A051451(n+1). - Tom Edgar, May 22 2014

Prog

(PARI) consecd(a) = {d = divisors(a); for (i=2, #d, if (d[i] - d[i-1] > 1, return(i-1)); ); return(a); }
findnext(a) = {nconsd = consecd(a); na = a + 1; while (consecd(na) < nconsd, na++); na; }
lista(nn) = {a = 1; print1(a, ", "); for (n=1, nn, a = findnext(a); print1(a, ", "); ); } \\ Michel Marcus, May 11 2014
(PARI)
first(n) = {
	my(res = vector(n), step = 1, oldm = 1, newm = 1);
	res[1] = 1;
	for(i = 2, n,
		while(res[i-1] % (newm+1) == 0,
			newm++;
		);
		if(newm > oldm,
			step = lcm([step, lcm([oldm..newm])]);
			oldm = newm
		);
		res[i] = res[i-1]+step
	);
	res
} \\ David A. Corneth, Jan 28 2024

Crossrefs

Cf. A003418, A051451, A080765, A368777.

Sequence in context: A141551 A181804 A094348 * A002182 A340840 A077006

Adjacent sequences: A242295 A242296 A242297 * A242299 A242300 A242301

Keyword

nonn

Author

J. Lowell, May 10 2014

Extensions

More terms from Michel Marcus, May 11 2014

Status

approved