John-Å. W. Olsen - cp's OEIS frontend

A225587 a(n) is the smallest prime of the form prime(n)*q + prime(n) + q, where q is an odd prime.

11, 23, 23, 31, 47, 83, 71, 79, 191, 179, 127, 151, 167, 263, 191, 431, 239, 743, 271, 431, 443, 479, 503, 359, 587, 1223, 1871, 431, 439, 683, 6143, 1583, 827, 839, 599, 607, 631, 983, 2351, 2087, 719, 727, 1151, 1163, 1187, 2399, 2543, 2687, 911, 919

Offset: 1

John-Å. W. Olsen, May 11 2013

The odd primes q minimizing prime(n)*q + prime(n) + q are listed in A225581.

			a(1) = 11 because prime(1) = 2 and the minimal prime of the form 2*q+2+q with q an odd prime is 11 = 2*3+2+3.

John-Å. W. Olsen, Table of a(n), for n = 1..1000

Cf. A225581, A000040.

a[n_] := Block[{q = 3, v, p = Prime@n},While[! PrimeQ[v = p q + p + q], q = NextPrime@q]; v]; Array[a, 50] (* Giovanni Resta, May 11 2013 *)

a(n) = (1+prime(n))*A225581(n) + prime(n).

a(26)-a(50) from Giovanni Resta, May 11 2013

A225626 Primes p such that floor(log(p)) + p^2 is prime.

Original entry on oeis.org

67, 73, 97, 103, 137, 431, 569, 709, 859, 929, 941, 971, 991, 1039, 22093, 22621, 22679, 22697, 22709, 22739, 22943, 22961, 22963, 23087, 23159, 23173, 23197, 23369, 23509, 23971, 24077, 24083, 24097, 24109, 24151, 24373, 24413, 24571, 24623, 24781, 24851

Offset: 1

John-Å. W. Olsen, May 11 2013

nonn

John-Å. W. Olsen, Table of n, a(n) for n = 1..5000

Cf. A225625.

Select[Prime[Range[3000]], PrimeQ[Floor[Log[#]] + #^2] &] (* T. D. Noe, May 13 2013 *)

A225659 Primes p where p + sumOfDigits(p) +- 3 is prime.

Original entry on oeis.org

2, 3, 5, 7, 23, 29, 41, 43, 47, 61, 67, 83, 89, 131, 137, 139, 157, 173, 179, 191, 197, 223, 227, 229, 241, 263, 269, 283, 311, 313, 317, 337, 353, 359, 373, 379, 397, 401, 409, 421, 443, 449, 463, 467, 487, 557

Offset: 1

John-Å. W. Olsen, May 11 2013

a(n) = A068690(n), A030144(n), A069556(n), A091727(n), A156756(n) if n<14.

			If p = 409, then 409 + sod(409) +- 3 = 409+13 - 3 = 419, which is prime.
If p =  23, then  23 + sod(23)  +- 3 = 23+5   + 3 = 31,  which is prime.

Andrew Howroyd, Table of n, a(n) for n = 1..394

Cf. A000040, A007605, A068690, A030144, A069556, A091727, A156756.

Select[Prime[Range[102]],Or@@PrimeQ[#+Total[IntegerDigits[#]]+{3,-3}] &] (* Jayanta Basu, May 23 2013 *)

ok(p)= {my(s=vecsum(digits(p)));isprime(p) && (isprime(p+s-3) || isprime(p+s+3))}
select(ok,[1..1000]) \\ Andrew Howroyd, Feb 22 2018

A225625 Primes of the form floor(log(p)) + p^2, where p is prime.

Original entry on oeis.org

4493, 5333, 9413, 10613, 18773, 185767, 323767, 502687, 737887, 863047, 885487, 942847, 982087, 1079527, 488100659, 511709651, 514337051, 515153819, 515698691, 517062131, 526381259, 527207531, 527299379, 533009579, 536339291, 536987939, 538100819, 546110171

Offset: 1

John-Å. W. Olsen, May 11 2013

nonn

			Floor(log(67)) + 67^2 = 4493.
Floor(log(22093)) + 22093^2 = 488100659.

John-Å. W. Olsen, Table of n, a(n) for n = 1..5000

Cf. A225626 (primes p).

p = Prime[Range[3000]]; Select[p^2 + Floor[Log[p]], PrimeQ] (* T. D. Noe, May 13 2013 *)

A225581 a(n) is the minimal odd prime q such that prime(n)*q + prime(n) + q is prime.

Original entry on oeis.org

3, 5, 3, 3, 3, 5, 3, 3, 7, 5, 3, 3, 3, 5, 3, 7, 3, 11, 3, 5, 5, 5, 5, 3, 5, 11, 17, 3, 3, 5, 47, 11, 5, 5, 3, 3, 3, 5, 13, 11, 3, 3, 5, 5, 5, 11, 11, 11, 3, 3, 7, 5, 3, 5, 3, 5, 5, 3, 5, 13, 11, 7, 3, 5, 11, 5, 3, 5, 5, 3, 19, 3, 3, 5, 29, 17, 3, 23, 3, 5, 7, 5, 5, 71, 3, 5, 5, 3, 3, 47, 3, 5, 3, 11, 3, 5, 3, 3, 11, 5, 23

Offset: 1

John-Å. W. Olsen, May 11 2013

			n = 1;  p = 2;  q = 3;
n = 2;  p = 3;  q = 5;
n = 3;  p = 5;  q = 3;
n = 4;  p = 7;  q = 3;

John-Å. W. Olsen, Table of n, a(n) for n = 1..1000

Cf. A000040.

a[n_] := Block[{q = 3, p = Prime@n},While[! PrimeQ[p*q + p + q], q = NextPrime@q]; q]; Array[a, 101] (* Giovanni Resta, May 11 2013 *)

a(n) = my(q=3, p=prime(n)); while(!isprime(p*q+p+q), q = nextprime(q+1)); q; \\ Michel Marcus, Sep 06 2021

from sympy import isprime, nextprime, prime
def a(n):
    q, p = 3, prime(n)
    while not isprime(p*q + p + q): q = nextprime(q)
    return q
print([a(n) for n in range(1, 102)]) # Michael S. Branicky, Sep 06 2021

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User: John-Å. W. Olsen

A225587 a(n) is the smallest prime of the form prime(n)*q + prime(n) + q, where q is an odd prime.

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A225626 Primes p such that floor(log(p)) + p^2 is prime.

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A225659 Primes p where p + sumOfDigits(p) +- 3 is prime.

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A225625 Primes of the form floor(log(p)) + p^2, where p is prime.

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A225581 a(n) is the minimal odd prime q such that prime(n)*q + prime(n) + q is prime.

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Author

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Mathematica

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