33247

Properties

Appears in sequences

• Let p be the n-th odd prime. a(n) is the least prime congruent to 7 modulo 8 such that Legendre(-a(n), q) = -Legendre(-1, q) for all odd primes q <= p.at n=7A001988
• a(n) = floor(tau*a(n-2)) + a(n-1) with a(0)=0 and a(1)=1.at n=19A005833
• Prime islands: for n >= 2, a(n) = least prime whose adjacent primes are exactly 2n apart; a(1) = 3 by convention.at n=31A046931
• Fifth term of weak prime sextet: p(m-3)-p(m-4) < p(m-2)-p(m-3) < p(m-1)-p(m-2) < p(m)-p(m-1) < p(m+1)-p(m).at n=11A054832
• Smallest prime(k) such that 2^n divides the product of composite numbers between prime(k) and prime(k+1) but 2^(n+1) does not.at n=44A077216
• a(n) is the smallest prime p of the form 4k+3 such that nextprime(p) - p = 4n.at n=9A082098
• "Lonely primes": those primes that are locally maximally isolated from the nearest other primes. The differences between each lonely prime and the immediately preceding prime and following primes are both greater than the corresponding differences for all lonely primes earlier in the sequence.at n=9A087770
• Primes p such that the largest prime factor of p^5 + 1 is less than p.at n=11A102327
• prime(k) for those k where floor((2*(prime(k+1)-prime(k))*PrimePi(k) mod (8*k))/k) = m with m = 11.at n=11A109565
• Numbers k such that k concatenated with k-7 gives the product of two numbers which differ by 9.at n=6A116114
• Numbers k such that k concatenated with k+1 gives the product of two numbers which differ by 7.at n=6A116167
• Numbers k such that k concatenated with k+7 gives the product of two numbers which differ by 5.at n=5A116207
• Numbers appearing in A122072 at least four times.at n=20A122390
• Primes p such that q-p = 40, where q is the next prime after p.at n=4A126721
• Primes p such that all the digits needed to write the consecutive Primes from 2 to p fill exactly a square (no holes, no overlaps).at n=37A158024
• Prime numbers with gaps larger than 18 towards both neighboring primes.at n=19A163111
• Prime numbers with gaps larger than 20 towards both neighboring primes.at n=7A163112
• Unique terms in sequence A210144.at n=42A214196
• Majority value maps: number of nX6 binary arrays indicating the locations of corresponding elements equal to at least half of their horizontal and antidiagonal neighbors in a random 0..1 nX6 array.at n=2A220384
• T(n,k)=Majority value maps: number of nXk binary arrays indicating the locations of corresponding elements equal to at least half of their horizontal and antidiagonal neighbors in a random 0..1 nXk array.at n=30A220386