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 A259417 Even powers of the odd primes listed in increasing order. 2
 1, 9, 25, 49, 81, 121, 169, 289, 361, 529, 625, 729, 841, 961, 1369, 1681, 1849, 2209, 2401, 2809, 3481, 3721, 4489, 5041, 5329, 6241, 6561, 6889, 7921, 9409, 10201, 10609, 11449, 11881, 12769, 14641, 15625, 16129, 17161, 18769, 19321, 22201, 22801, 24649 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Each of the following sequences, p^(q-1) with p >= 2 and q > 2 primes, except their respective first elements, powers of 2, is a subsequence: A001248(p) = p^2,  A030514(p) = p^4,  A030516(p) = p^6, A030629(p) = p^10, A030631(p) = p^12, A030635(p) = p^16, A030637(p) = p^18, A137486(p) = p^22, A137492(p) = p^28, A139571(p) = p^30, A139572(p) = p^36, A139573(p) = p^40, A139574(p) = p^42, A139575(p) = p^46, A173533(p) = p^52, A183062(p) = p^58, A183085(p) = p^60. See also the link to the OEIS Wiki. The sequences A053182(n)^2, A065509(n)^4, A163268(n)^6 and A240693(n)^10 are subsequences of this sequence. The odd numbers in A023194 are a subsequence of this sequence. LINKS Hartmut F. W. Hoft, Table of n, a(n) for n = 1..473 EXAMPLE a(11) = 5^4 = 625 is followed by a(12) = 3^6 = 729 since no even power of an odd prime falls between them. MATHEMATICA a259417[bound_] := Module[{q, h, column = {}}, For[q = Prime, q^2 <= bound, q = NextPrime[q], For[h = 1, q^(2*h) <= bound, h++, AppendTo[column, q^(2*h)]]]; Prepend[Sort[column], 1]] a259417 (* data *) With[{upto=25000}, Select[Union[Flatten[Table[Prime[Range[2, Floor[ Sqrt[ upto]]]]^n, {n, 0, Log[2, upto], 2}]]], #<=upto&]] (* Harvey P. Dale, Nov 25 2017 *) CROSSREFS Sequence in context: A348742 A016754 A110487 * A030156 A331587 A192775 Adjacent sequences:  A259414 A259415 A259416 * A259418 A259419 A259420 KEYWORD nonn AUTHOR Hartmut F. W. Hoft, Jun 26 2015 STATUS approved

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Last modified January 28 23:12 EST 2022. Contains 350670 sequences. (Running on oeis4.)