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 A297961 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 left- and right-concatenating a digit to the a(n-1) primes obtained in the previous iteration. 2
 4, 11, 20, 53, 51, 100, 63, 76, 42, 43, 20, 13, 4, 4, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS No 16-digit numbers can be obtained from the 15-digit number 889292677731979. LINKS Prime Curios, 889292677731979 EXAMPLE 1-digit 2-digit 3-digit 4-digit ... 15-digit --------------------------------------------------------------- 2 3 13 131 2131 6131 137 2137 3137 9137 139 4139 23 233 5233 8233 239 2239 9239 43 431 5431 8431 9431 433 1433 3433 7433 9433 439 1439 9439 53 73 733 1733 3733 4733 6733 9733 739 3739 9739 83 839 5839 8839 9839 5 7 17 173 6173 9173 179 2179 5179 8179 37 373 1373 3373 4373 6373 379 6379 47 479 5479 9479 67 673 3673 4673 6673 7673 677 2677 889292677731979 3677 8677 9677 97 971 2971 6971 8971 977 6977 --------------------------------------------------------------- a(1) = 4, a(2) = 11, a(3) = 20, a(4) = 53, ..., a(15)= 1. MATHEMATICA Block[{b = 10, t}, t = Select[Range[b], CoprimeQ[#, b] &]; TakeWhile[Length /@ Fold[Function[{a, n}, Append[a, If[EvenQ[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 == 1: 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, A297960, A298048. Sequence in context: A075099 A240784 A345434 * A240155 A161975 A272042 Adjacent sequences: A297958 A297959 A297960 * A297962 A297963 A297964 KEYWORD nonn,full,base,fini AUTHOR Seiichi Manyama, Jan 09 2018 STATUS approved

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Last modified March 30 23:40 EDT 2023. Contains 361623 sequences. (Running on oeis4.)