A256355 Composites in base 10 that remain composite in exactly three bases b, 2 <= b <= 10, expansions interpreted as decimal numbers.

11233, 42241, 98281, 131239, 161953, 315151, 358135, 606553, 692263, 785851, 1114081, 1130419, 1525777, 1906363, 3369313, 3403081, 3880873, 5616721, 6036103, 6947611, 7253191, 7516783, 7886593, 8799127, 8811223, 9108289, 9113203, 9195313, 9450361, 9600769

Offset: 1

Author

Sebastian Petzelberger, Mar 25 2015

Keywords

• nonn
• base

Examples

			11233 = 324413_5 and 324413_10 is composite; 11233 = 44515_7 and 44515_10 is composite; 11233_10 itself is composite. Interpreted in base 2, 3, 4, 6, 8, and 9 the result is prime. Hence 11233 is in this sequence.
		

Links

• Sebastian Petzelberger, Table of n, a(n) for n = 1..10000
• Carlos Rivera, PP&P Puzzle 24: Primes in several bases

Crossrefs

Cf. A052026, A256350, A256351, A256352, A256353, A256354, A256356, A038537, A052027, A052028, A052029, A052030, A052031, A052032, A052033, A084482, A236356.

Programs

PARI

is(n)=!isprime(n) && sum(b=2,9,isprime(fromdigits(digits(n,b))))==6 \\ Charles R Greathouse IV, Apr 23 2015