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 A352312 Start of the first run of exactly n consecutive primes using only prime digits. 1
 7, 223, 37253, 2, 2575723, 7533777323, 277535577223, 5323733533375237, 57552737757357223 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS This is a variant of A343471. LINKS Chris K. Caldwell and G. L. Honaker, Jr., Prime Curios! 277535577223. EXAMPLE a(1) = 7 because it is the first prime using only prime digits and whose next prime 11 does not use only prime digits. a(3) = 37253 because 37253, 37273, 37277 is the first run of 3 consecutive primes using only prime digits, then next prime 37307 has a digit 0. PROG (Python) from sympy import nextprime, isprime from itertools import count, islice, product def onlypd(n): return set(str(n)) <= set("2357") def agen():     adict, n = {1:7, 4:2}, 1     yield 7     for digits in count(2):         for p in product("2357", repeat=digits-1):             for end in "37":                 t0 = t = int("".join(p) + end)                 run = 0                 while isprime(t):                     run += 1                     t = nextprime(t)                     if not onlypd(t): break                 if run not in adict:                     adict[run] = t0                     if run > n:                         for r in range(n+1, run+1):                             if r in adict:                                 yield adict[r]                                 n += 1 print(list(islice(agen(), 6))) # Michael S. Branicky, Mar 11 2022 CROSSREFS Cf. A082755, A343471. Subsequence of A019546. Sequence in context: A202655 A009488 A302059 * A138247 A322709 A015506 Adjacent sequences:  A352309 A352310 A352311 * A352313 A352314 A352315 KEYWORD nonn,base,more AUTHOR Bernard Schott, Mar 11 2022 EXTENSIONS a(9) from Michael S. Branicky, Mar 15 2022 STATUS approved

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Last modified August 10 03:38 EDT 2022. Contains 356029 sequences. (Running on oeis4.)