A082869 - OEIS

%I #10 Aug 26 2021 19:15:03

%S 4,7,9,13,19,23,37,71,89,97,131,167,193,227,229,257,263,269,271

%N 3^n - 2^n is a semiprime.

%C a(20) >= 653. - _Max Alekseyev_, Aug 26 2021

%H P. C. Leyland, <a href="http://www.leyland.vispa.com/numth/factorization/anbn/main.htm">Homogeneous Cunningham numbers</a>.

%H <a href="http://factordb.com/index.php?query=3%5E653-2%5E653">Status of 3^653-2^653 in factordb.com</a>.

%e a(1) = 4 because 3^4 - 2^4 = 5 * 13

%e a(2) = 7 because 3^7 - 2^7 = 29 * 71

%e a(3) = 9 because 3^9 - 2^9 = 1009 * 19

%e a(4) = 13 because 3^13 - 2^13 = 53 * 29927

%e a(5) = 19 because 3^19 - 2^19 = 1559 * 745181

%e a(6) = 23 because 3^23 - 2^23 = 47 * 2002867877

%e a(7) = 37 because 3^37 - 2^37 = 8891471 * 50642213021

%e a(8) = 71 because 3^71 - 2^71 = 67049419 * 111998979662707645844109121

%e a(9) = 89 because 3^89 - 2^89 = 4120081168939 * 706132008101135602203621405289

%e a(10) = 97 because 3^97 - 2^97 = 319128643 * 59813046375181769306016700165290169537

%e a(11) = 131 because 3^131 - 2^131 = 263 * 1210399177182288006201752262354382648158190136861552303421773

%e a(12) = 167 because 3^167 - 2^167 = 167884386911 * 284602839755962600307038183361142274453177384697761703968640951718869

%e a(13) = 193 because 3^193 - 2^193 = 773 * 157116815095122696291789672145814943987605497895096234870661710074857006307174092298131047

%e a(14) = 227 because 3^227 - 2^227 = 167360891302418779411 * 12102381564694515014432350438002672779054341887509579790377508212702751544613632122970969

%e a(15) = 229 because 3^229 - 2^229 = 271117470516046849 * 67237232094433305864393166477037402086197319313004074022941345112953840883539481643687544179

%e a(16) = 257 because 3^257 - 2^257 = 3650201327 * 114247220844165289049224917003868019618046824570124111266639206512722372880755761151052076786187552795911804402733

%e a(17) = 263 because 3^263 - 2^263 = 1789696394587605010251024191 * 169867630212703250249981022070263878299079238108093021871181171428200213741587995035055139427113909

%e a(18) = 269 because 3^269 - 2^269 = 3767 * 58833122596041019850277965408508940208380870952125838087379156948993498251689923575161076689330121444393974916753840891087813

%e a(19) = 271 because 3^271 - 2^271 = 2711 * 735750407736473144959046057264728365874119021724332398617327934122565857164514694088659506296666818455309890905079155116415309

%Y Cf. A001047, A001358, A057468, A058765, A050244, A095027.

%K more,hard,nonn

%O 1,1

%A _Hugo Pfoertner_, May 24 2003

%E More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Dec 30 2007