34123

Properties

Appears in sequences

• Smallest prime p such that there is a gap of 2n between p and previous prime.at n=30A001632
• Number of nonempty subsets of {1,2,...,n} in which exactly 1/3 of the elements are <= n/3.at n=17A047194
• Duplicate of A047194.at n=17A048039
• Number of nonempty subsets of {1,2,...,n} in which exactly 1/3 of the elements are <= (n+2)/3.at n=17A048072
• a(n) = 2*p + 2*n - 1, where p is the least prime such that next_prime(2*p) - 2*p = 2*n - 1.at n=20A059847
• a(n) = 2*p + 2*n - 1, where p is the least prime such that next_prime(2*p) - 2*p = 2*n - 1.at n=28A059847
• Smallest prime p such that there is a gap of 2*prime(n) between p and previous prime.at n=10A080083
• Primes that show the slow decrease in the larger values of the Andrica function Af(k) = sqrt(p(k+1)) - sqrt(p(k)), where p(k) denotes the k-th prime.at n=11A084975
• Smallest prime which occurs exactly n times in the sequence A086527.at n=29A086528
• Primes p such that the polynomial x^5-x^4-x^3-x^2-x-1 mod p has 5 distinct zeros.at n=24A106281
• Primes that do not divide any term of the Lucas 5-step sequence A074048.at n=11A106301
• Primes of the form i*prime(i) + (i+1)*prime(i+1).at n=25A119487
• Prime numbers p for which quintonacci quintic polynomial x^5-x^4-x^3-x^2-x-1 modulus p is completely factorizable.at n=25A135846
• Prime numbers p not of the form 10k+1 for which the quintonacci quintic polynomial x^5 - x^4 - x^3 - x^2 - x - 1 modulus p is factorizable into five binomials.at n=20A135847
• Primes at the upper end of the gaps mentioned in A144104.at n=41A144105
• Linking prime for the second and third member of maximal chains of primes that have at least three members.at n=7A145651
• a(n) is the smallest number not already in the sequence, such that the concatenation of all a(n) displays the periodic digit string 1, 2, 3, 4 (and repeat).at n=17A165302
• a(n) is the smallest prime q such that, for the previous prime p and the following prime r, the fraction (r-q)/(q-p) has denominator n in lowest terms.at n=30A179234
• Primes occurring in A213521.at n=34A213522
• Primes p of the form penta(n)-3, where penta(n) is the n-th pentagonal number.at n=36A232537