A181333 a(n) cannot be prefixed or followed by any digit to form a semiprime.
60, 208, 252, 552, 588, 630, 656, 696, 710, 768, 816, 864, 1025, 1028, 1050, 1225, 1280, 1300, 1432, 1804, 1950, 2004, 2016, 2152, 2160, 2376, 2410, 2664, 2672, 2808, 2920, 2988, 3172, 3230, 3356
Offset: 1
Examples
a(1) = 60 because 60 (any digit to the left still gives a multiple of 10, not a semiprime) and 601 is prime, 602 = 2 * 7 * 43, 603 = 3^2 * 67, 604 = 2^2 * 151, 605 = 5 * 11^2, 606 = 2 * 3 * 101, 607 is prime, 608 = 2^5 * 19, 609 = 3 * 7 * 29. a(2) = 208 because any digit to the left still ends in 8, and is nonsemiprime, and: 2081 is prime, 2082 = 2 * 3 * 347, 2083 is prime, 2084 = 2^2 * 521, 2085 = 3 * 5 * 139, 2086 = 2 * 7 * 149, 2087 is prime, 2088 = 2^3 * 3^2 * 29, 2089 is prime.
Links
- Robert Israel, Table of n, a(n) for n = 1..10000
Crossrefs
Cf. A001358.
Programs
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Maple
filter:= proc(n) local i,r; r:= 10^(1+ilog10(n)); not ormap(t -> numtheory:-bigomega(t)=2, [seq(i*r+n, i=1..9),seq(10*n+i,i=0..9)]) end proc: select(filter, [$1..10000]); # Robert Israel, Feb 02 2025
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Mathematica
fQ[n_] := Block[{d = Range[0, 9], id = IntegerDigits@ n}, Union[ semiPrimeQ@ # & /@ Sort@ Join[ FromDigits /@ (Join[{#}, id] & /@ d), FromDigits /@ (Join[id, {#}] & /@ d)]] == {False}]; Select [ Range@ 100, fQ] ; (* Robert G. Wilson v, Jan 27 2011 *)
Comments