A113567
Numbers n such that prime(n) +- n, prime(n) +- 2n and prime(n) +- 3n are all primes.
Original entry on oeis.org
252420, 874650, 1413510, 2053380, 2298240, 2456160, 4640370, 7529340, 8708910, 11205390, 18734310, 22141980, 23680650, 26407920, 30866010, 31340400, 38515050, 43242780, 44584260, 58430400, 61172790, 62739180, 64449210
Offset: 1
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t = {}; p = 2*3*5*7; Do[ If[ PrimeQ[Prime[p*n] - p*3n] && PrimeQ[Prime[p*n] - p*2n] && PrimeQ[Prime[p*n] - p*n] && PrimeQ[Prime[p*n] + p*n] && PrimeQ[Prime[p*n] + p*2n] && PrimeQ[Prime[p*n] + p*3n], AppendTo[t, n]], {n, 2194723}]; p*t
A113568
Numbers k such that prime(k) +- k, prime(k) +- 2k, prime(k) +- 3k and prime(k) +- 4k are all primes.
Original entry on oeis.org
2053380, 794006430, 1659273630, 3621510480, 3725013180, 4361365470, 4993201710, 7311363150, 7865614680, 9934880340, 10608361260, 12818200500, 13499311980, 13940598420, 14241904320, 14463052170, 14601895770, 18668815620, 19102545000, 20336611050, 20706006090, 21322649670, 22595831580
Offset: 1
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t = {}; p = 2*3*5*7; Do[ If[ PrimeQ[Prime[p*n] - p*3n] && PrimeQ[Prime[p*n] - p*2n] && PrimeQ[Prime[p*n] - p*n] && PrimeQ[Prime[p*n] + p*n] && PrimeQ[Prime[p*n] + p*2n] && PrimeQ[Prime[p*n] + p*3n], AppendTo[t, n]], {n, 17 106}]; p*t
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list(lim) = {my(k = 0, q); forprime(p = 1, lim, k++; q = 1; for(i = -4, 4, if(i != 0 && !isprime(p + i*k), q = 0; break)); if(q, print1(k,", ")));} \\ Amiram Eldar, Jul 12 2025
A113569
Least number k such that k is a multiple of A034386(2*n) and p-(n-1)*k, p-(n-2)*k, ... p-2*k, p-k, p, p+k, p+2*k, ... p+(n-2)*k, and p+(n-1)*k are all prime, with p being the k-th prime.
Original entry on oeis.org
2, 6, 720, 252420, 2053380
Offset: 1
a(1) = 2 which is a multiple of the primorial A034386(2) = 2.
a(2) = 6 because p = 13, p-6 = 7, and p+6 = 19 are all prime and 6 is a multiple of A034386(4) = 6.
a(3) = 720 because p = 5443, p-720 = 4723, p-2*720 = 4003, p+720 = 6163, and p+2*720 = 6883 are all prime and 720 is a multiple of A034386(6) = 30.
Showing 1-3 of 3 results.
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