This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A378018 #17 Dec 23 2024 13:50:21 %S A378018 3,5,7,11,13,17,19,23,29,37,53,67,83,97,113,127,157,173,199,409,431, %T A378018 619,641,829,1039,1061,1249,1459,1481,1669,1879,1901,2089,2111,2297, %U A378018 6917,9227,13873,16183,18493,23087,25423,27733,30013,30047,60077,90073 %N A378018 Primes p which can be written as p = (A060735(k) +- next largest prime factor not in A060735(k)) for some k. %C A378018 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. %C A378018 31 is the first prime this does not produce (other than 2). %C A378018 143 is the first nonprime value that this pattern produces (other than values < 3). %C A378018 Conjectured to be infinite. %F A378018 (not in order) primorial(i) * m +- prime(i+1) where 0<m<prime(i+1). %e A378018 23 is a term because 23 = 2*3*5 - 7 and it is prime. %e A378018 67 is a term because 67 = 2*2*3*5 + 7 and it is prime. %o A378018 (PARI) rad(n) = factorback(factorint(n)[, 1]); %o A378018 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 %Y A378018 Cf. A060735, subset of A000040, superset of A367182, superset of A038708. %K A378018 nonn %O A378018 1,1 %A A378018 _Daniel D Gibson_, Nov 14 2024