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A158979 a(n) is the smallest number > n such that n^4 + a(n)^4 is prime. 12
2, 3, 4, 5, 8, 7, 10, 9, 10, 13, 16, 13, 14, 15, 22, 17, 20, 23, 24, 29, 38, 29, 26, 41, 26, 27, 28, 33, 34, 37, 32, 37, 34, 35, 52, 37, 38, 39, 46, 41, 50, 53, 44, 47, 58, 55, 50, 55, 60, 61, 62, 61, 56, 55, 58, 59, 68, 61, 62, 73, 66, 77, 64, 67, 84, 71, 68, 69, 74, 83, 84, 73 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

For exponent 2 instead of 4 see A089489: Pythagorean triple has a prime hypotenuse.

Corresponding sequences with odd exponent u are impossible: x^u + y^u has factor x+y.

a(2k-1) is even, a(2k) is odd, a(n)-n is odd.

Conjecture: a(n) exists for all n, i.e., the sequence is well-defined and infinite.

Conjecture: a(n)-n = 1 for infinitely many n.

The largest value of a(n)-n for n <= 100 occurs at n = 90: 121-90 = 31.

a(n)-n = 1 for 35 values of n <= 100.

LINKS

Table of n, a(n) for n=1..72.

EXAMPLE

1^4 + 2^4 = 17 is prime, so a(1) = 2.

2^4 + 3^4 = 97 is prime, so a(2) = 3.

5^4 + 6^4 = 1921 = 17*113, 5^4 + 7^4 = 3026 = 2*17*89, 5^4 + 8^4 = 4721 is prime, so a(5) = 8.

PROG

(MAGMA) S:=[]; for n in [1..72] do q:=n^4; k:=n+1; while not IsPrime(q+k^4) do k+:=1; end while; Append(~S, k); end for; S; // Klaus Brockhaus, Apr 12 2009

CROSSREFS

Cf. A089489.

Sequence in context: A319605 A245822 A069797 * A233249 A330573 A309369

Adjacent sequences:  A158976 A158977 A158978 * A158980 A158981 A158982

KEYWORD

easy,nonn

AUTHOR

Ulrich Krug (leuchtfeuer37(AT)gmx.de), Apr 01 2009

EXTENSIONS

Edited and entries verified by Klaus Brockhaus, Apr 12 2009

STATUS

approved

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Last modified October 21 23:34 EDT 2021. Contains 348160 sequences. (Running on oeis4.)