A034809 -id:A034809 - cp's OEIS frontend

A034808 Concatenation of 'prevprime(k) and k' is a prime.

3, 9, 37, 39, 51, 63, 87, 89, 111, 117, 123, 153, 157, 163, 173, 177, 183, 207, 211, 213, 217, 219, 239, 249, 257, 263, 267, 269, 273, 277, 279, 289, 321, 323, 327, 333, 337, 339, 343, 359, 369, 379, 407, 423, 439, 441, 459, 471, 473, 477, 479, 489, 497, 513

Offset: 1

Patrick De Geest, Oct 15 1998

Since there are primes in the sequence, and concat(p,p) = p*(10^x+1) is always composite, it is clear that here the variant 2 (A151799(n) < n) of the prevprime function is used, rather than the variant 1 (A007917(n) <= n). - M. F. Hasler, Sep 09 2015

			n=333 -> previous prime is 331, thus '331333' is a prime.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A034809-A034821.

Cf. A151799, A007917.

coQ[n_]:=PrimeQ[FromDigits[Flatten[IntegerDigits[{NextPrime[n,-1],n}]]]]; Select[Range[3,513],coQ[#]&] (* Jayanta Basu, May 30 2013 *)
Select[Range[2,550],PrimeQ[NextPrime[#,-1]*10^IntegerLength[#]+#]&] (* Harvey P. Dale, Nov 22 2020 *)

isok(n)=n>2 && isprime(fromdigits(concat(digits(precprime(n-1)), digits(n)))) \\ Andrew Howroyd, Aug 13 2024

from sympy import isprime, prevprime
def aupto(m):
  return [k for k in range(3, m+1) if isprime(int(str(prevprime(k))+str(k)))]
print(aupto(513)) # Michael S. Branicky, Mar 09 2021

Offset changed by Andrew Howroyd, Aug 13 2024

A034595 Concatenation of 'nextprime(a(n)) and a(n)' and 'a(n) and nextprime(a(n))' are both prime.

Original entry on oeis.org

27, 51, 63, 123, 199, 217, 219, 233, 257, 341, 353, 357, 417, 423, 429, 473, 501, 519, 523, 551, 579, 597, 609, 653, 657, 667, 669, 687, 703, 717, 777, 783, 801, 873, 891, 971, 987, 1017, 1043, 1139, 1157, 1161, 1271, 1337, 1343, 1389, 1671, 1973, 2019

Offset: 1

Patrick De Geest, Oct 15 1998

			a(n)=353 -> nextprime(a(n)) is 359 so '353359' and '359353' are both prime.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Intersection of A034591 and A034594.

Cf. A034596, A034808, A034809, A034814.

bpQ[n_]:=Module[{np=NextPrime[n]},AllTrue[{n*10^IntegerLength[np]+ np, np* 10^IntegerLength[ n]+n}, PrimeQ]]; Select[Range[2100],bpQ] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, May 19 2016 *)

Offset changed by Andrew Howroyd, Aug 13 2024

A034814 Concatenations C1 and C2 are both prime (see the comment lines).

Original entry on oeis.org

9, 51, 63, 87, 111, 123, 153, 177, 207, 211, 239, 263, 273, 289, 327, 333, 343, 359, 407, 471, 489, 497, 513, 541, 597, 621, 651, 659, 663, 681, 687, 693, 697, 747, 753, 793, 819, 831, 869, 909, 977, 987, 1027, 1041, 1089, 1131, 1143, 1239, 1491, 1611

Offset: 1

Patrick De Geest, Oct 15 1998

C1 = 'prevprime(k) followed by k'.

C2 = 'k followed by prevprime(k)'.

			n=747 -> previous prime is 743, thus '743747' and '747743' are both primes.

Andrew Howroyd, Table of n, a(n) for n = 1..1000

Intersection of A034808 and A034809.

Cf. A034810-A034821.

Offset changed by Andrew Howroyd, Aug 13 2024

cp's OEIS Frontend

A034808 Concatenation of 'prevprime(k) and k' is a prime.

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A034595 Concatenation of 'nextprime(a(n)) and a(n)' and 'a(n) and nextprime(a(n))' are both prime.

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A034814 Concatenations C1 and C2 are both prime (see the comment lines).

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