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 A119680 Prime numbers obtained by inserting a 0 between each pair of adjacent digits of a prime number > 10. 1
 101, 103, 107, 109, 307, 401, 503, 509, 601, 607, 701, 709, 809, 907, 10007, 10009, 10103, 10301, 10501, 10607, 10709, 10903, 10909, 20101, 20507, 20707, 20903, 30103, 30307, 30509, 30703, 30803, 30809, 40009, 40507, 40709, 50707, 50909, 60103, 60107, 60509 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS From Rémy Sigrist, Oct 08 2017: (Start) See A159236 for the original prime numbers. The least prime numbers > 10 remaining prime during exactly k iterations of the operation of inserting a 0 between each pair of adjacent digits are, for small values of k: k prime - ----- 0 23 1 11 2 19 3 17 4 220333 5 8677267 (End) LINKS Table of n, a(n) for n=1..41. EXAMPLE The first four terms arise from 11 -> 101, 13 -> 103, 17 -> 107, 19 -> 109. 23 -> 203 is not prime, so 203 is not a term. MATHEMATICA a = Table[Table[Mod[Floor[Prime[m]/10^n], 10], {n, 4, 0, -1}], {m, 5, 200}]; Dimensions[a] b = Table[Sum[(If[Mod[n - 1, 2] == 0, a[[m, 1 + Floor[(n - 1)/2]]], 0])*10^(9 - n), {n, 1, 9}], {m, 1, 195}]; c = Flatten[Table[If[PrimeQ[b[[m]]], b[[m]], {}], {m, 1, 195}]] PROG (PARI) forprime (p=10, 599, if (isprime(pp=fromdigits(digits(p), 100)), print1 (pp ", "))) \\ Rémy Sigrist, Oct 08 2017 (Python) from itertools import count, islice from sympy import isprime, nextprime def ok(n): return n > 10 and isprime(n) and isprime(int("0".join(list(str(n))))) def agen(): p = 11 while True: t = int("0".join(list(str(p)))) if isprime(t): yield t p = nextprime(p) print(list(islice(agen(), 50))) # Michael S. Branicky, Jul 11 2022 CROSSREFS Cf. A159236. Sequence in context: A309488 A134809 A256186 * A329737 A166571 A201965 Adjacent sequences: A119677 A119678 A119679 * A119681 A119682 A119683 KEYWORD nonn,base AUTHOR Roger L. Bagula, Jun 11 2006 EXTENSIONS Name edited by Rémy Sigrist, Oct 08 2017 a(39)-a(41) from Michael S. Branicky, Jul 11 2022 STATUS approved

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Last modified December 3 07:48 EST 2023. Contains 367531 sequences. (Running on oeis4.)