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A109018 Least n-almost prime number which gives a different n-almost prime number when digits are reversed. 11
13, 15, 117, 126, 270, 2576, 8820, 16560, 21168, 46848, 295245, 441600, 846720, 4078080, 80663040, 40590720, 2173236480, 4011724800, 21122906112, 40915058688, 274148425728, 63769149440, 2707602702336, 6167442456576 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

An emirp ("prime" spelled backwards) is a prime whose (base 10) reversal is also prime, but which is not a palindromic prime. The first few are 13, 17, 31, 37, 71, 73, 79, 97, 107, 113, 149, 157, ... (A006567).

An emirpimes ("semiprime" spelled backwards) is a semiprime whose (base 10) reversal is a different semiprime. A list of the first emirpimeses (or "semirpimes") are 15, 26, 39, 49, 51, 58, 62, 85, 93, 94, 115, 122, 123, ... (A097393).

An "emirp tsomla-3" ("3-almost prime" spelled backwards) is the k=3 sequence of the series for which k=1 are emirps and k=2 are emirpimes, a list of these being A109023. The union of these for k=1 through k = 13 is A109019.

The primes correspond to the "1-almost prime" numbers 2, 3, 5, 7, 11, ... (A000040). The 2-almost prime numbers correspond to semiprimes 4, 6, 9, 10, 14, 15, 21, 22, ... (A001358).

The first few 3-almost primes are 8, 12, 18, 20, 27, 28, 30, 42, 44, 45, 50, 52, 63, 66, 68, 70, 75, 76, 78, 92, 98, 99, ... (A014612). The first few 4-almost primes are 16, 24, 36, 40, 54, 56, 60, 81, 84, 88, 90, 100, ... (A014613).

The first few 5-almost primes are 32, 48, 72, 80, ... (A014614).

The Mathematica code for this was written by Ray Chandler who has coauthorship credit for this sequence.

LINKS

Table of n, a(n) for n=1..24.

Eric Weisstein's World of Mathematics, Almost Prime.

Eric Weisstein's World of Mathematics, Emirp.

Eric Weisstein and Jonathan Vos Post, Emirpimes.

EXAMPLE

a(1) = 13 because 13 is the smallest "emirp" (prime which, digits reversed, becomes a different prime) since reverse(13) = 31 is prime.

a(2) = 15 because 15 is the smallest emirpimes ("semiprime" spelled backwards) as a semiprime whose (base 10) reversal is a different semiprime. The first such number is 15, since 15 reversed is 51 and both 15 and 51 are semiprimes (i.e. 15 = 3 * 5 and 51 = 3 * 17).

a(3) = 117 because 117 is the smallest "emirp tsomla-3" ("3-almost prime" spelled backwards) since 117 reversed is 711 and 117 = 3^2 * 13 and 711 = 3^2 * 79.

MATHEMATICA

kAlmost[n_] := Plus @@ Last /@ FactorInteger@n; fQ[n_] := Block[{id = IntegerDigits@n, k = kAlmost@n}, If[id != Reverse@id && k == kAlmost@FromDigits@Reverse@id, k, -1]]; t = Table[0, {20}]; Do[ a = fQ@n; If[a < 20 && t[[a]] == 0, t[[a]] = n; Print[{a, n}]], {n, 10, 150000000}] (* Robert G. Wilson v *)

CROSSREFS

Cf. A006567, A097393, A109023, A109023, A109024, A109025, A109026, A109027, A109028, A109029, A109030, A109031.

Sequence in context: A299593 A318543 A302001 * A237912 A268664 A158697

Adjacent sequences:  A109015 A109016 A109017 * A109019 A109020 A109021

KEYWORD

base,nonn,less

AUTHOR

Jonathan Vos Post, Jun 16 2005

EXTENSIONS

a(14)-a(16) from Robert G. Wilson v, Jan 06 2008

a(17)-a(24) from Donovan Johnson, Nov 17 2008

STATUS

approved

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Last modified September 20 02:19 EDT 2021. Contains 347577 sequences. (Running on oeis4.)