A068712 -id:A068712 - cp's OEIS frontend

A068713 Numbers k for which 10*2^k + 3 is a prime (giving terms of A068712).

0, 1, 2, 3, 4, 6, 7, 10, 11, 17, 19, 25, 27, 31, 33, 42, 43, 49, 51, 57, 64, 65, 106, 139, 196, 273, 279, 379, 392, 505, 663, 737, 874, 943, 1015, 1546, 1547, 1686, 3937, 4065, 5164, 6257, 6401, 7066, 7412, 7966, 9440, 9921, 11105, 15076, 15547, 22646, 24779

Offset: 1

Amarnath Murthy, Mar 05 2002

nonn

Cf. A068712.

Select[Range[0,4100], PrimeQ[10*2^#+3] &] (* Jayanta Basu, May 22 2013 *)

More terms from Sascha Kurz, Mar 17 2002
Extended by Charles R Greathouse IV, Apr 24 2010
Offset 1 from Michel Marcus, Jan 10 2023

A068715 Primes of the form 10*3^k + 1.

Original entry on oeis.org

11, 31, 271, 811, 21871, 196831, 5314411, 3874204891, 313810596091, 46383976865881019793281501678905914543189676980091, 2738927449953408337773479392637715347860807235997334411

Offset: 1

Amarnath Murthy, Mar 05 2002

nonn

			21871 is a member as it is a concatenation of 2187 (= 3^7) and 1.

Vincenzo Librandi, Table of n, a(n) for n = 1..19

Cf. A068712, A068714.

[a: n in [0..200] | IsPrime(a) where a is 10*3^n + 1]; // Vincenzo Librandi, Dec 08 2011

Select[Table[10*3^n+1,{n,0,300}],PrimeQ](* Vincenzo Librandi, Dec 08 2011 *)

More terms from Sascha Kurz, Mar 17 2002

A068714 Primes formed from a concatenation of 2 and 3^k for some k.

Original entry on oeis.org

23, 29, 227, 281, 2243, 2729, 26561, 219683, 24782969, 210460353203, 2282429536481, 27625597484987, 250031545098999707, 279766443076872509863361, 2239299329230617529590083, 219383245667680019896796723, 2202755595904452569706561330872953769

Offset: 0

Amarnath Murthy, Mar 05 2002

			2243 is a member as it is a concatenation of 2 and 243 = 3^5.

Cf. A068712.

Select[Table[FromDigits[Prepend[IntegerDigits[3^n],2]],{n,75}],PrimeQ] (* Jayanta Basu, May 22 2013 *)

More terms from Sascha Kurz, Mar 17 2002

A068801 Primes that can be formed by concatenating 2^a and 3^b.

Original entry on oeis.org

11, 13, 19, 23, 29, 41, 43, 83, 89, 127, 163, 181, 227, 281, 641, 643, 827, 881, 1283, 1289, 1627, 2243, 2729, 4243, 4729, 6427, 6481, 8243, 10243, 16561, 16729, 20483, 26561, 40961, 42187, 81929, 86561, 102481, 163841, 166561, 219683, 326561, 327689, 859049

Offset: 1

Amarnath Murthy, Mar 05 2002

			8243 is a concatenation of 2^3 and 3^5. 10242187 is a term as a concatenation of 1024 (=2^10) and 2187(=3^7).

Michael S. Branicky, Table of n, a(n) for n = 1..8482

Cf. A068712, A068714.

from sympy import isprime
from itertools import count, takewhile
def auptod(digits):
    M = 10**digits
    pows2 = list(takewhile(lambda x: x < M , (2**a for a in count(0))))
    pows3 = list(takewhile(lambda x: x < M , (3**b for b in count(0))))
    strs2, strs3 = list(map(str, pows2)), list(map(str, pows3))
    concat = (int(s2+s3) for s2 in strs2 for s3 in strs3)
    return sorted(set(t for t in concat if t < M and isprime(t)))
print(auptod(6)) # Michael S. Branicky, Aug 17 2022

Corrected and extended by Larry Reeves (larryr(AT)acm.org), Jun 25 2002

a(43) and beyond from Michael S. Branicky, Aug 17 2022

cp's OEIS Frontend

A068713 Numbers k for which 10*2^k + 3 is a prime (giving terms of A068712).

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A068715 Primes of the form 10*3^k + 1.

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A068714 Primes formed from a concatenation of 2 and 3^k for some k.

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A068801 Primes that can be formed by concatenating 2^a and 3^b.

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