A036341
Concatenation of prime p and nextprime(p) is prime -> cycles of 4 steps possible.
Original entry on oeis.org
127787377, 1510818931, 3147482977, 3307903909, 3621408103, 3964636549, 7224979183, 7881628361, 8043354509, 8740618759, 10091655397, 10164789521, 10194261067, 10380609119, 10436432219, 11472028801, 12059694769, 13887362681, 14880879703, 15197340049
Offset: 1
Offset corrected and terms a(6) and beyond added by
Giovanni Resta, May 14 2020
A036340
Concatenation of prime p and nextprime(p) is prime -> cycles of 3 steps possible.
Original entry on oeis.org
467, 941, 959941, 3396199, 4858943, 5696101, 6475643, 7566133, 7584253, 7592261, 9305281, 9463877, 11430491, 13442243, 14374837, 15941473, 17414497, 17691997, 19584223, 21421849, 22310159, 22808459, 27601163, 29198881
Offset: 0
A334885
Let q = p | p' be the digit concatenation of a prime p with its prime successor. If the result is a prime repeat the construction setting p = q. a(n) is the smallest prime for which this can be repeated exactly n times.
Original entry on oeis.org
3, 2, 13681, 467, 127787377, 200603842261
Offset: 0
Let "|" denote concatenation.
3 | 5 = 35, which is not prime, so a(0) = 3.
2 | 3 = 23 (prime), 23 | 29 = 2329 (composite), so a(1) = 2.
13681 | 13687 (prime), 1368113687 | 1368113699 (prime), 13681136871368113699 | 13681136871368113711 (composite), so a(2) = 13681.
-
a[n_] := Block[{pp=1, p, q, c=-1}, While[ c!=n, c=0; p = pp = NextPrime@ pp; While[ PrimeQ[ q = FromDigits[ Join @@ IntegerDigits@{p, NextPrime@ p}]], c++; p = q]]; pp]; a /@ Range[0, 3]
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