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A109019 Numbers whose digit reversal is different and has the same number of prime factors (with multiplicity). 3
13, 15, 17, 26, 31, 37, 39, 49, 51, 58, 62, 71, 73, 79, 85, 93, 94, 97, 107, 113, 115, 117, 122, 123, 126, 129, 143, 147, 149, 155, 157, 158, 159, 165, 167, 169, 177, 178, 179, 183, 185, 187, 199, 203, 205, 221, 225, 226, 244, 246, 265, 270, 285, 286, 289, 290 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

This sequence is the union of emirps, emirpimes, "emirp tsomla-3", "emirp tsomla-4", "emirp tsomla-5" and so forth. 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. He also has more values.

LINKS

Table of n, a(n) for n=1..56.

Eric Weisstein's World of Mathematics, Almost Prime.

Eric Weisstein's World of Mathematics, Emirp.

Eric Weisstein and Jonathan Vos Post, Emirpimes.

FORMULA

{A006567} U {A097393} U (A109023} U {A109024} U ... U {A109131} U ...

MATHEMATICA

Select[Range[400], # != FromDigits[Reverse[IntegerDigits[ # ]]] && Sum[FactorInteger[ # ][[i, 2]], {i, 1, Length[FactorInteger[ # ]]}] == Sum[FactorInteger[ FromDigits[Reverse[IntegerDigits[ # ]]]][[i, 2]], {i, 1, Length[FactorInteger[FromDigits[Reverse[IntegerDigits[ # ]]]]]}] &] (* Stefan Steinerberger, Jun 16 2007 *)

CROSSREFS

Cf. A006567, A097393, A109018, A109023-A109131.

Sequence in context: A031060 A120129 A341329 * A068893 A079829 A096090

Adjacent sequences:  A109016 A109017 A109018 * A109020 A109021 A109022

KEYWORD

nonn,base

AUTHOR

Jonathan Vos Post, Jun 16 2005

EXTENSIONS

More terms from Stefan Steinerberger, Jun 16 2007

STATUS

approved

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Last modified September 17 16:49 EDT 2021. Contains 347487 sequences. (Running on oeis4.)