1,1

Up to 10^7, members are 3^3, 3^4, 3^5, 3^8, 3^9, 3^10, 3^11, 3^12, 3^13, 7^3, 7^4, 7^5, 7^6, 13^3, 13^4, 13^5, 43^2, 43^3, 67^2, 73^2, 79^2, 127^2, 151^2, 163^2, 193^2, 211^2, ..., . - Robert G. Wilson v (rgwv(at)rgwv.com), May 12 2006

In the first 23 members of A000959, {1, 3, 7, 9, 13, 15, 21, 25, 31, 33, 37, 43, 49, 51, 63, 67, 69, 73, 75, 79, 87, 93, 99}, 3 is a prime lucky number (A031157), 3^2 is also a lucky number but 3^3=27 and 3^4=81 are not lucky numbers so that are members of this sequence.

lst = Range[1, 2*10^7, 2]; i = 2; While[i <= (len = Length[lst]) && (k = lst[[i]]) <= len, lst = Drop[lst, {k, len, k}]; i++ ]; p = Select[lst, PrimeQ@# &]; lst2 = {}; Do[k = 1; lmt = Floor@Log[ p[[n]], 10^7]; t = Table[p[[n]]^i, {i, 2, lmt}]; While[k < lmt - 1, If[ !MemberQ[lst, t[[k]] ], AppendTo[lst2, t[[k]] ]]; k++ ], {n, Length@p}]; Sort@lst2 - Robert G. Wilson v (rgwv(at)rgwv.com), May 12 2006

Cf. A031157, A000959.

Sequence in context: A126381 A129254 A034033 this_sequence A008884 A031455 A045004

Adjacent sequences: A057606 A057607 A057608 this_sequence A057610 A057611 A057612

more,nonn

Naohiro Nomoto (6284968128(AT)geocities.co.jp), Oct 09 2000

More terms from Robert G. Wilson v (rgwv(at)rgwv.com), May 12 2006