A378018 Primes p which can be written as p = (A060735(k) +- next largest prime factor not in A060735(k)) for some k.

3, 5, 7, 11, 13, 17, 19, 23, 29, 37, 53, 67, 83, 97, 113, 127, 157, 173, 199, 409, 431, 619, 641, 829, 1039, 1061, 1249, 1459, 1481, 1669, 1879, 1901, 2089, 2111, 2297, 6917, 9227, 13873, 16183, 18493, 23087, 25423, 27733, 30013, 30047, 60077, 90073

Offset

1,1

Comments

A060735 can be thought of as multiples of primorials, up to the next prime not found in the given primorial. This sequence adds or subtracts that next prime to produce new prime values.

31 is the first prime this does not produce (other than 2).

143 is the first nonprime value that this pattern produces (other than values < 3).

Conjectured to be infinite.

Links

Table of n, a(n) for n=1..47.

Formula

(not in order) primorial(i) * m +- prime(i+1) where 0<m<prime(i+1).

Example

23 is a term because 23 = 2*3*5 - 7 and it is prime.
67 is a term because 67 = 2*2*3*5 + 7 and it is prime.

Prog

(PARI) rad(n) = factorback(factorint(n)[, 1]);
lista(nn) = my(a=1, list = List()); for (n=2, nn, my(f = factor(a), p = if (a==1, 2, nextprime(vecmax(f[, 1])+1))); if (isprime(a-p), listput(list, a-p)); if (isprime(a+p), listput(list, a+p)); a = a + rad(a); ); vecsort(Set(list)); \\ Michel Marcus, Dec 14 2024

Crossrefs

Cf. A060735, subset of A000040, superset of A367182, superset of A038708.

Sequence in context: A363286 A120637 A278454 * A064534 A139758 A306084

Adjacent sequences: A378015 A378016 A378017 * A378019 A378020 A378021

Keyword

nonn,new

Author

Daniel D Gibson, Nov 14 2024

Status

approved