Rashid Naimi has authored 4 sequences.
A339174
Let b(1) = 2 and let b(n+1) be the least prime expressible as k*(b(n)-1)*b(n)+1; this sequence gives the values of k in order.
Original entry on oeis.org
1, 1, 1, 2, 5, 9, 6, 79, 16, 219, 580, 387, 189, 7067, 1803, 6582, 31917, 18888, 20973, 132755, 11419, 50111
Offset: 1
[Corrected by _Peter Munn_, Nov 05 2022]
For p = 2, the smallest k for which f(k) = k*(p-1)*p+1 is prime is 1 because we have: f(1) = k*(p-1)*p+1 = 1*(2-1)*2+1 = 3.
This sets p = 3 for the next iteration for which the smallest k for which f(k) is prime is 1: f(1) = k*(p-1)*p+1 = 1*(3-1)*3+1 = 7.
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my(p=2, k=1); while(1, my(runningP=k*(p-1)*p+1); if(ispseudoprime(runningP), print1(k, ", "); k=1; p=runningP; , k=k+1))
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my(k=[1, 1, 1, 2, 5, 9, 6, 79, 16, 219, 580, 387, 189, 7067, 1803, 6582, 31917, 18888, 20973, 132755, 11419, 50111], p=2); for(i=1, #k, p=k[i]*(p-1)*p+1); print("\n", p, "\n"); \\ to produce the P587124 prime
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from sympy import isprime
A339174_list, a = [2], 2
while len(A339174_list) < 10:
k, c, b = 1, 1, (a-1)*a
while True:
c += b
if isprime(c):
A339174_list.append(k)
a = c
break
k += 1 # Chai Wah Wu, Dec 04 2020
A306601
Let b(1) = 3 and let b(n+1) be the least prime expressible as k*(b(n)-1)*b(n)-1; this sequence gives the values of k in order.
Original entry on oeis.org
1, 1, 2, 4, 8, 16, 5, 360, 142, 104, 34, 1904, 3127, 253, 1219, 8755, 16222, 7672, 22515
Offset: 1
For p = 3, the smallest k for which f(k) = k*(p-1)*p-1 is prime is 1:
f(1) = k*(p-1)*p-1 = 1*(3-1)*3-1 = 5.
This sets p = 5 for the next iteration for which the smallest k for which f(k) is prime is 1:
f(1) = k*(p-1)*p-1 = 1*(5-1)*5-1 = 19.
This sets p = 19 for the next iteration for which the smallest k for which f(k) is prime is 2:
f(2) = k*(p-1)*p-1 = 2*(19-1)*19-1 = 683.
This sets p = 683 for the next iteration for which the smallest k for which f(k) is prime is 4:
f(4) = k*(p-1)*p-1 = 4*(683-1)*683-1 = 1863223.
This sets p = 1863223 for the next iteration for which the smallest k for which f(k) is prime is 8:
f(8) = k*(p-1)*p-1 = 8*(1863223-1)*1863223-1 = P14.
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p=3; k=1; while(1, runningP=k*(p-1)*p-1; if(ispseudoprime(runningP), print1(k,", "); k=1; p=runningP;, k=k+1))
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/* The largest prime (P242682) can be generated by using the code: */ k=[1, 1, 2, 4, 8, 16, 5, 360, 142, 104, 34, 1904, 3127, 253, 1219, 8755, 16222, 7672, 22515]; p=3; for(i=1, #k, p=k[i]*(p-1)*p-1); print("\n", p, "\n")
A319224
Integers q for which f(q) = ((((q - 2)! - 1) / q) - 1) / (q + 1) is a prime number.
Original entry on oeis.org
7, 11, 19, 61, 2557
Offset: 1
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a[q_]:=If[PrimeQ[((((q - 2)! - 1) / q) - 1) / (q + 1)], q]; DeleteCases[Array[a, 100], Null] (* Stefano Spezia, Nov 04 2018 *)
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forprime(q=7, 2557, my(p = ((((q - 2)! - 1) / q) - 1) / (q + 1)); if(ispseudoprime(p), print1(q, ", ")))
A319304
Integers q for which f(q) = ((((q - 1)! + 1) / q) + 1) / (q + 1) is a prime number.
Original entry on oeis.org
7, 17, 31, 67, 89
Offset: 1
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[n: n in [1..100] | IsPrime(n) and IsPrime((((Factorial(n-1)+1) div n)+1) div (n+1))]; // Vincenzo Librandi, Sep 21 2018
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Select[Prime[Range[100]], PrimeQ[((((# - 1)! + 1) / #) + 1) / (# + 1)] &] (* Vincenzo Librandi, Sep 21 2018 *)
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forprime(q=7, 89, my(p = ((((q - 1)! + 1) / q) + 1) / (q + 1)); if(ispseudoprime(p), print1(q, ", ")))
1621 and 1699, which do not belong here, removed by
Rashid Naimi, Mar 21 2019
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