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

Author

Giovanni Teofilatto, Apr 06 2007

Keywords

• easy
• nonn
• changed

Examples

			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.
		

Crossrefs

Cf. A001597 (perfect powers).

Programs

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 */

Extensions

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