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 A298048 a(1) = number of 1-digit primes (that is, 4: 2,3,5,7); then a(n) = number of distinct n-digit prime numbers obtained by left- or right-concatenating a digit to the a(n-1) primes obtained in the previous iteration. 1
 4, 16, 70, 243, 638, 1450, 2819, 4951, 7629, 10677, 13267, 15182, 15923, 15796, 14369, 12547, 10291, 7939, 5703, 3911, 2559, 1595, 920, 561, 321, 167, 72, 37, 11, 6, 3 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS EXAMPLE 2-digit primes: ------------------- 23   2->23 or 3->23 29   2->29 13   3->13 43   3->43 53   3->53 or 5->53 73   3->73 or 7->73 83   3->83 31   3->31 37   3->37 or 7->37 59   5->59 17   7->17 47   7->47 67   7->67 97   7->97 71   7->71 79   7->79 ------------------- a(2) = 16. =================== 3-digit primes: [223, 233, 523, 823, 239, 229, 293, 829, 929, 113, 131, 313, 613, 137, 139, 311, 331, 431, 631, 317, 433, 443, 643, 743, 439, 353, 653, 853, 953, 173, 373, 733, 673, 773, 739, 337, 937, 379, 283, 383, 683, 883, 983, 839, 359, 593, 659, 859, 599, 617, 179, 271, 571, 971, 719, 347, 547, 647, 947, 479, 167, 367, 467, 677, 967, 197, 397, 797, 977, 997] In the case of 223, 2->23 (adding the rightmost digit)->223 (adding the leftmost digit) and 2, 23 and 223 are prime. In the case of 233, 2->23 (adding the rightmost digit)->233 (adding the rightmost digit) and 2, 23 and 233 are prime. In the case of 523, 2->23 (adding the rightmost digit)->523 (adding the leftmost digit) and 2, 23 and 523 are prime. a(3) = 70. MATHEMATICA Block[{b = 10, t}, t = Select[Range[b], CoprimeQ[#, b] &]; TakeWhile[Length /@ Fold[Function[{a, n}, Append[a, Union[Join @@ {Join @@ Map[Function[k, Select[Map[Prepend[k, #] &, Range[b - 1]], PrimeQ@ FromDigits[#, b] &]], Last[a]], Join @@ Map[Function[k, Select[Map[Append[k, #] &, t], PrimeQ@ FromDigits[#, b] &]], Last[a]]}] ] ] @@ {#1, #2} &, {IntegerDigits[Prime@ Range@ PrimePi@ b, b]}, Range[2, 40]], # > 0 &]] (* Michael De Vlieger, Jan 21 2018 *) PROG (Ruby) require 'prime' def A298048(n)   ary = [2, 3, 5, 7]   a_ary = [4]   (n - 1).times{|i|     ary1 = []     ary.each{|a|       (1..9).each{|d|         j = d * 10 ** (i + 1) + a         ary1 << j if j.prime?         j = a * 10 + d         ary1 << j if j.prime?       }     }     ary = ary1.uniq     a_ary << ary.size   }   a_ary end p A298048(10) CROSSREFS Cf. A050986, A050987, A297960, A297961. Sequence in context: A231297 A231358 A000303 * A144316 A180145 A133789 Adjacent sequences:  A298045 A298046 A298047 * A298049 A298050 A298051 KEYWORD nonn,fini,full,base AUTHOR Seiichi Manyama, Jan 11 2018 EXTENSIONS a(16)-a(31) from Michael De Vlieger, Jan 21 2018 STATUS approved

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Last modified July 22 14:40 EDT 2019. Contains 325222 sequences. (Running on oeis4.)