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A127913 Least k >= 0 such that A001597(n)+k is an even semiprime. 3

%I

%S 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,

%T 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,

%U 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

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

%e 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.

%e 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.

%o (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 */

%Y Cf. A001597 (perfect powers).

%K easy,nonn

%O 1,1

%A _Giovanni Teofilatto_, Apr 06 2007

%E Edited, corrected and extended by _Klaus Brockhaus_, Apr 09 2007

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Last modified January 19 04:56 EST 2022. Contains 350464 sequences. (Running on oeis4.)