A236356 -id:A236356 - cp's OEIS frontend

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

Sebastian Petzelberger, Mar 25 2015

			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.

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

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

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

A377181 Rectangular array, by antidiagonals: (row 1) = r(1) = A002808 (composite numbers); (row n) = r(n) = A002808(r(n-1)) for n>=1.

Original entry on oeis.org

4, 6, 9, 8, 12, 16, 9, 15, 21, 26, 10, 16, 25, 33, 39, 12, 18, 26, 38, 49, 56, 14, 21, 28, 39, 55, 69, 78, 15, 24, 33, 42, 56, 77, 94, 106, 16, 25, 36, 49, 60, 78, 105, 125, 141, 18, 26, 38, 52, 69, 84, 106, 140, 164, 184, 20, 28, 39, 55, 74, 94, 115, 141, 183, 212, 236

Offset: 1

Clark Kimberling, Oct 19 2024

			 corner:
   4     6     8     9    10    12    14    15    16    18
   9    12    15    16    18    21    24    25    26    28
  16    21    25    26    28    33    36    38    39    42
  26    33    38    39    42    49    52    55    56    60
  39    49    55    56    60    69    74    77    78    84
  56    69    77    78    84    94   100   105   106   115
  78    94   105   106   115   125   133   140   141   152

Cf. A002808 (row 1), A050545 (row 2), A280327 (row 3), A006508 (column 1), A022450 (column 2), A023451 (column 3), A059981, A236356, A280327 (principal diagonal), A377173, A114577 (dispersion of the composite numbers).

c[n_] := c[n] = Select[Range[500], CompositeQ][[n]]
r[0] = Table[c[n], {n, 1, 10}]
r[n_] := r[n] = c[r[n - 1]]
Grid[Table[r[n], {n, 0, 6}]]  (* array *)
p[n_, k_] := r[n][[k]];
Table[p[n - k + 1, k], {n, 0, 9}, {k, n + 1, 1, -1}] // Flatten  (* sequence *)

A059981(n) = number of appearances of A002808(n).

cp's OEIS Frontend

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

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