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 A297960 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 alternately right- and left-concatenating a digit to the a(n-1) primes obtained in the previous iteration. 2
 4, 9, 30, 49, 99, 74, 101, 71, 72, 35, 28, 9, 4 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS No 14-digit numbers can be obtained from the four 13-digit numbers counted by a(13). LINKS EXAMPLE 1-digit 2-digit 3-digit 4-digit ... 13-digit ------------------------------------------------------------ 2 23 223 2237 2239 523 5231 5233 5237 823 8231 8233 6638182333331 8237 29 229 2293 2297 829 8291 8293 8297 929 9293 3 31 131 1319 331 3313 3319 431 631 6311 5981563119937 6317 37 137 1373 337 3371 3373 937 9371 9377 5 53 353 3533 3539 653 853 8537 8539 953 9533 9539 59 359 3593 659 6599 859 8597 8599 7 71 271 2711 2713 2719 571 5711 5717 971 9719 73 173 1733 373 3733 3739 673 6733 8313667333393 6737 773 79 179 379 3793 2682637937713 3797 479 4793 4799 ------------------------------------------------------------ a(1) = 4, a(2) = 9, a(3) = 30, a(4) = 49, ..., a(13) = 4. MATHEMATICA Block[{b = 10, t}, t = Select[Range[b], CoprimeQ[#, b] &]; TakeWhile[Length /@ Fold[Function[{a, n}, Append[a, If[OddQ[n], Join @@ Map[Function[k, Select[Map[Prepend[k, #] &, Range[9]], 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, 16]], # > 0 &]] (* Michael De Vlieger, Jan 20 2018 *) PROG (Python) from sympy import isprime def alst(): primes, alst = [2, 3, 5, 7], [] while len(primes) > 0: alst.append(len(primes)) if len(alst)%2 == 0: candidates = set(int(d+str(p)) for p in primes for d in "123456789") else: candidates = set(int(str(p)+d) for p in primes for d in "1379") primes = [c for c in candidates if isprime(c)] return alst print(alst()) # Michael S. Branicky, Apr 11 2021 CROSSREFS Cf. A050986, A050987, A297961, A298048. Sequence in context: A241393 A186650 A091658 * A295910 A086688 A309295 Adjacent sequences: A297957 A297958 A297959 * A297961 A297962 A297963 KEYWORD nonn,full,base,fini AUTHOR Seiichi Manyama, Jan 09 2018 STATUS approved

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Last modified February 6 12:03 EST 2023. Contains 360104 sequences. (Running on oeis4.)