A158979 -id:A158979 - cp's OEIS frontend

A244950 Least number k > n such that k^128 + n^128 is prime.

120, 113, 106, 259, 304, 85, 212, 135, 158, 47, 62, 985, 84, 47, 518, 485, 178, 169, 106, 27, 88, 139, 632, 47, 44, 643, 194, 209, 606, 1529, 32, 113, 1094, 139, 754, 647, 38, 45, 262, 69, 94, 631, 90, 527, 326, 195, 54, 277, 232, 187, 554, 189, 78, 799, 216, 131, 1132, 173

Offset: 1

Derek Orr, Jul 08 2014

nonn

a(n) = n+1 iff n is in A215431.

			The n-value for which n^128 + 1 is prime (sequence A056994) is n = 120 (where n > 1 by definition). Thus a(1) = 120.

Jens Kruse Andersen, Table of n, a(n) for n = 1..1000

Cf. A158979, A089489, A242557.

lnk[n_]:=Module[{k=n+1,n128=n^128},While[!PrimeQ[n128+k^128],k++];k]; Array[lnk,60] (* Harvey P. Dale, Apr 22 2018 *)

a(n)=for(k=n+1,10^4,if(isprime(k^128+n^128),return(k)))
n=1;while(n<100,print1(a(n),", ");n++)

import sympy
from sympy import isprime
def a(n):
    for k in range(n+1,10**4):
        if isprime(k**128+n**128):
            return k
for n in range(1, 100):
    print(a(n), end=', ')

A160026 Primes p such that p^4 + 17^4 + 3^4 is prime.

Original entry on oeis.org

13, 29, 37, 59, 89, 101, 107, 241, 263, 293, 373, 409, 569, 683, 821, 971, 1033, 1187, 1229, 1277, 1289, 1423, 1511, 1627, 1759, 1823, 1901, 1907, 1973, 2011, 2069, 2083, 2099, 2207, 2311, 2473, 2593, 2633, 2707, 2719, 2753, 2819, 3023, 3137, 3209, 3221

Offset: 1

Ulrich Krug (leuchtfeuer37(AT)gmx.de), Apr 30 2009

For primes p, q, r the sum p^4 + q^4 + r^4 can be prime only if at least one of p, q, r equals 3. This sequence is the special case q = 17, r = 3.
It is conjectured that the sequence is infinite.
There are consecutive primes (1901, 1907) in the sequence.

			p = 3: 3^4 + 17^4 + 3^4 = 83683 = 67*1249, so 3 is not in the sequence.
p = 1901: 1901^4 + 17^4 + 3^4 = 13059557751203 is prime, so 1901 is in the sequence.
p = 1907: 1907^4 + 17^4 + 3^4 = 13225216032803 is prime, so 1907 is in the sequence.

Cf. A158979, A159829, A160022.

[ p: p in PrimesUpTo(3250) | IsPrime(p^4+83602) ]; // Klaus Brockhaus, May 03 2009

Edited, 409 inserted and extended beyond 2069 by Klaus Brockhaus, May 03 2009

cp's OEIS Frontend

A244950 Least number k > n such that k^128 + n^128 is prime.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Python