A113117 a(1) = 2; for n>1, a(n) is the smallest integer > a(n-1) such that all primes <= a(n-1) divide at least one integer k for a(n-1) < k <= a(n).

2, 4, 6, 10, 15, 26, 46, 86, 166, 326, 634, 1262, 2518, 5006, 10006, 19946, 39874, 79738, 159398, 318778, 637502, 1274998, 2549978, 5099902, 10199786, 20399534, 40799062, 81598082, 163196134, 326392258, 652784498, 1305568942, 2611137838, 5222275634, 10444551254

Offset

1,1

Comments

It appears that A113118 and this sequence agree except for the 5th term.

Links

Table of n, a(n) for n=1..35.

Example

The primes <= a(5) = 15 are 2, 3, 5, 7, 11 and 13. So a(6) is the smallest integer >15 such that each prime <= 15 divides at least one integer between 16 and a(6). Setting a(6) to 26 = 2*13 satisfies the conditions. (2 divides 16. 3 divides 18. 5 divides 20. 7 divides 21. 11 divides 22. And 13 divides 26.)

Prog

(PARI) {m=21; print1(a=2, ", "); for(n=2, m, nxt=a+1; forprime(p=1, a, k=a+1; while(k%p>0, k++); nxt=max(nxt, k)); print1(a=nxt, ", "))} \\ Klaus Brockhaus, Jan 07 2006
(Python)
from sage.all import primes
n, a = 1, 2
data = ""
while True:
    print(n, a)
    data += str(a) + ", "
    if len(data) > 262: print(data[:-2]); break
    n += 1
    a = max((a//p) * p + p for p in list(primes(a+1)))
# Lucas A. Brown, Feb 22 2024

Crossrefs

Cf. A113118.

Sequence in context: A167270 A355108 A060168 * A179531 A134682 A327408

Adjacent sequences: A113114 A113115 A113116 * A113118 A113119 A113120

Keyword

nonn

Author

Leroy Quet, Jan 03 2006

Extensions

a(8)-a(21) from Klaus Brockhaus, Jan 07 2006

a(22)-a(35) from Lucas A. Brown, Feb 22 2024

Status

approved