A178755 Integers that become semiprime when any single digit is removed.

44, 46, 49, 64, 66, 69, 94, 96, 99, 104, 155, 215, 221, 222, 225, 226, 251, 255, 262, 265, 333, 334, 335, 338, 339, 349, 355, 358, 385, 393, 394, 395, 469, 515, 551, 555, 557, 558, 577, 585, 587, 622, 625, 655, 695, 774, 777, 822, 825, 826, 855, 857, 862, 865

Offset: 1

Author

Jonathan Vos Post, Jun 09 2010

Keywords

• base
• nonn

Comments

The subsequence of semiprimes begins: 46, 49, 69, 94, 155, 215, 221, 226, 262, 265, 334, 335, 339, 355, 358, 393, 394, 395, 469, 515, 551, 622, 655, 695, 862, 865, 914, 933, 934, 951, 955, 1111, 1115, 1119, 1159, 1219, 1411, 1415, 1466, 2021, 2026, 2062, 2095, 2159, 2899, 2959, 2995, 2998, 3035, 3039, ....

The subsequence of primes begins: 251, 349, 557, 577, 587, 857, 877, 1559, 1669, 4111, 4973, 5051, 5119, 5519, 5591, 6299, 6679, 6871, 6899, 6949, 7213, 7789, 7949, 7993, 8669, 8699, 9133, 9221, 9551, 9749, ....

This is to semiprimes A001358 as A034895 is to primes A000040. Note that this is not a subset of A107342, as there are values with nonsemiprime digits, beginning with 104, 155, 215, 221, 222, ....

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A001358, A034895, A107342.

Programs

Mathematica

 Select[Range[3000],Union[PrimeOmega[FromDigits/@Subsets[IntegerDigits[#],{IntegerLength[#]-1}]]]=={2}&] (* Harvey P. Dale, Apr 25 2015 *)

Formula

a(10) = 104 because deleting the "1" gives "04" which by OEIS protocol becomes the semiprime 4=2*2; deleting the "0" gives the semiprime 14=2*7; and deleting the "4" gives the semiprime 10=2*5.

Extensions

Extended by Ray Chandler