A036341 -id:A036341 - cp's OEIS frontend

A036339 Concatenation of prime p and nextprime(p) is prime -> cycles of 2 steps possible.

467, 941, 13681, 14461, 21787, 22171, 22369, 24049, 24151, 25457, 29333, 37397, 41221, 42467, 43481, 46511, 48023, 54133, 56681, 68699, 75883, 85081, 101341, 103511, 117443, 120193, 126199, 137363, 144323, 145133, 158791, 175853, 181891, 183797

Offset: 1

Patrick De Geest, Dec 15 1998

C. Rivera, Details of procedure

Cf. A030459, A034592, A036340, A036341.

Offset corrected and missing 181891 inserted by Sean A. Irvine, Oct 26 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

Patrick De Geest, Dec 15 1998

Terms from 3396199 up to 17691997 found by Jo Yeong Uk (hyukjo(AT)sigma.chungnam.ac.kr).

Carlos Rivera, Puzzle 29. Pi = P i-1&nxtprm(P i-1), Pi = prime for i => 1, The Prime Puzzles & Problems Connection.

Cf. A030459, A034593, A036339, A036341.

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

Giovanni Resta, May 14 2020

a(6) > 10^13.

			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.

Carlos Rivera, Puzzle 29. P_i = P_(i-1) & nxtprm(P_(i-1)), P_i = prime for i => 1, The Prime Puzzles and Problems Connection.

Cf. A030459, A034593, A036339, A036340, A036341.

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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A036339 Concatenation of prime p and nextprime(p) is prime -> cycles of 2 steps possible.

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A036340 Concatenation of prime p and nextprime(p) is prime -> cycles of 3 steps possible.

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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.

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