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

Author

Daniel D Gibson, Nov 14 2024

Keywords

• nonn

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.

Examples

			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.
		

Crossrefs

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

Programs

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

Formula

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

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