A127913 Least k >= 0 such that A001597(n)+k is an even semiprime.

3, 0, 2, 1, 6, 1, 7, 2, 2, 9, 10, 1, 6, 1, 9, 6, 2, 9, 6, 2, 1, 11, 6, 9, 2, 3, 1, 22, 5, 18, 2, 9, 10, 1, 18, 5, 10, 1, 14, 13, 6, 18, 5, 18, 1, 10, 15, 13, 10, 1, 18, 25, 26, 2, 9, 6, 1, 14, 6, 7, 9, 9, 2, 1, 18, 1, 18, 2, 9, 2, 21, 9, 6, 5, 22, 11, 1, 2, 1, 18, 5, 10, 1, 2, 13, 42, 1, 18, 5, 1, 2

Offset

1,1

Links

Table of n, a(n) for n=1..91.

Example

A001597(5) = 16. Among 16+0 = 16, 16+1 = 17, 16+2 = 18 = 2*3*3, 16+3 = 19, 16+4 = 20 = 2*2*5, 16+5 = 21 = 3*7 there is no even semiprime, but 16+6 = 22 = 2*11 is an even semiprime. Hence a(5) = 6.
A001597(14) = 121. 121+0 = 121 = 11*11 is not even, but 121+1 = 122 = 2*61 is an even semiprime. Hence a(14) = 1.

Prog

(Magma) PP:=[1] cat [ n: n in [2..5184] | IsPower(n) ]; [ k: p in PP | exists(k) {x: x in [0..100000] | IsEven(p+x) and IsPrime((p+x) div 2) } ]; /* Klaus Brockhaus, Apr 09 2007 */

Crossrefs

Cf. A001597 (perfect powers).

Sequence in context: A084196 A295041 A359710 * A135991 A331422 A279631

Adjacent sequences: A127910 A127911 A127912 * A127914 A127915 A127916

Keyword

easy,nonn

Author

Giovanni Teofilatto, Apr 06 2007

Extensions

Edited, corrected and extended by Klaus Brockhaus, Apr 09 2007

Status

approved