A337687 a(1) = 2; for n > 1, a(n) = smallest number not occurring earlier which shares a prime factor with a(n-1) and also has a prime factor which is not a factor of a(n-1).

2, 6, 10, 12, 14, 18, 15, 20, 22, 24, 21, 28, 26, 30, 33, 36, 34, 38, 40, 35, 42, 39, 45, 48, 44, 46, 50, 52, 54, 51, 57, 60, 55, 65, 70, 58, 56, 62, 66, 63, 69, 72, 68, 74, 76, 78, 75, 80, 82, 84, 77, 88, 86, 90, 85, 95, 100, 92, 94, 96, 87, 93, 99, 102, 98, 91, 104, 106, 108, 105, 110, 112

Offset

1,1

Comments

Like A336957 no prime or prime power can be a term as if it shared a prime factor with the previous term it would then not contain a prime factor not in the previous term. It is likely all other composite numbers appear.

Links

Scott R. Shannon, Table of n, a(n) for n = 1..1000

Example

a(2) = 6 as 2*3 = 6, where 2 is a prime factor shared with a(1) = 2 and 3 is a prime factor which is not a factor of a(1).
a(3) = 10 as 2*5 = 10, where 2 is a prime factor shared with a(2) = 6 and 5 is a prime factor which is not a factor of a(2).
a(4) = 12 as 2*2*3 = 12, where 2 is a prime factor shared with a(3) = 10 and 3 is a prime factor which is not a factor of a(3).

Prog

(PARI)
isok(k, fprec, v) = {if (#select(x->(x==k), v) == 0, my(f = Set(factor(k)[, 1]), finter = setintersect(f, fprec)); #setintersect(f, fprec) && #setminus(f, fprec); ); }
lista(nn) = {my(va= vector(nn)); va[1] = 2; for (n=2, nn, my(k=2, fprec = Set(factor(va[n-1])[, 1])); while (! isok(k, fprec, va), k++); va[n] = k; ); va; } \\ Michel Marcus, Nov 30 2020

Crossrefs

Cf. A000961, A064413, A336957, A098550, A020639, A280864.

Sequence in context: A298748 A139799 A214586 * A305634 A139710 A194712

Adjacent sequences: A337684 A337685 A337686 * A337688 A337689 A337690

Keyword

nonn

Author

Scott R. Shannon, Nov 28 2020

Status

approved