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

1,1

Comments

Analogy: semiprimes A001358 are to primes A000040 as this sequence is to A032734.

Number of terms less than or equal to 10^n: 0, 1, 12, 144, 2203, 31408, 422176, ..., . For those which are less than 10^6 (mod 10), {{0, 8392}, {8, 4700}, {2, 6173}, {6, 4717}, {4, 4708}, {5, 2384}, {7, 94}, {3, 79}, {9, 81}, {1, 80}}. - Robert G. Wilson v, Jan 27 2011

Links

Table of n, a(n) for n=1..35.

Example

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.

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 *)

Crossrefs

Cf. A001358.

Sequence in context: A249911 A292223 A112827 * A082529 A126248 A224335

Adjacent sequences: A181330 A181331 A181332 * A181334 A181335 A181336

Keyword

nonn,easy,base

Author

Jonathan Vos Post, Jan 27 2011

Status

approved