A032672 -id:A032672 - cp's OEIS frontend

A099678 Numbers n such that 10n01 is a prime.

3, 5, 6, 15, 17, 20, 21, 23, 27, 30, 38, 47, 48, 54, 56, 57, 65, 68, 71, 72, 83, 84, 90, 92, 102, 105, 110, 116, 122, 126, 134, 135, 143, 155, 156, 162, 164, 173, 182, 183, 197, 198, 200, 201, 203, 204, 210, 213, 222, 225, 227, 231, 233, 236, 249, 261, 264, 270, 281, 282, 290

Offset: 1

N. J. A. Sloane, Nov 19 2004

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A032672, A100502 (for the primes).

t0:=[]; u0:=[]; for n from 0 to 500 do p0:="10"; p1:="01"; t1:=cat(p0,n,p1); t1:=convert(t1,decimal,10); if isprime(t1) then t0:=[op(t0),n]; u0:=[op(u0),t1]; fi; od: t0;
# Alternative:
filter:= n -> isprime( 10^(ilog10(n)+4)+100*n+1):
select(filter, [$1..1000]); # Robert Israel, Mar 16 2017

Select[ Range[280], PrimeQ[ FromDigits[Join[{1, 0}, IntegerDigits[ # ], {0, 1}]]] &] (* Robert G. Wilson v, Nov 20 2004 *)

isok(n) = isprime(eval(concat(concat("10", n), "01"))); \\ Michel Marcus, Jul 29 2015

A099744 Palindromes n such that 10n01 is a prime.

Original entry on oeis.org

3, 5, 6, 222, 282, 353, 434, 555, 626, 656, 747, 828, 858, 929, 939, 10301, 10601, 11411, 11711, 12821, 12921, 13431, 13731, 14141, 14241, 14741, 15951, 16161, 17171, 17771, 18381, 18981, 19191, 19491, 19991, 20402, 20702, 22022, 22322

Offset: 1

N. J. A. Sloane, Nov 19 2004

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

Cf. A002113, A099746, A032672, A099720, A100026, A100027.

read transforms; pal:=[]; for n from 0 to 8000 do if digrev(n) = n then pal:=[op(pal),n]; fi; od:
t0:=[]; u0:=[]; for n from 1 to nops(pal) do m:=pal[n]; p0:="10"; p1:="01"; t1:=cat(p0,m,p1); t1:=convert(t1,decimal,10); if isprime(t1) then t0:=[op(t0),m]; u0:=[op(u0),t1]; fi; od: t0; # u0 gives A099746.

p = Select[ Range[ 22322], # == FromDigits[ Reverse[ IntegerDigits[ # ]]] &]; Select[p, PrimeQ[ FromDigits[ Join[{1, 0}, IntegerDigits[ # ], {0, 1}]]] &] (* Robert G. Wilson v, Nov 20 2004 *)
Select[Range[23000],PalindromeQ[#]&&PrimeQ[FromDigits[Join[{1,0},IntegerDigits[ #],{0,1}]]]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Mar 26 2021 *)

More terms from Robert G. Wilson v, Nov 19 2004

A032667 Digit '4' concatenated with a(n) is a prime.

Original entry on oeis.org

1, 3, 7, 19, 21, 31, 33, 39, 43, 49, 57, 61, 63, 67, 79, 87, 91, 99, 111, 127, 129, 133, 139, 153, 157, 159, 177, 201, 211, 217, 219, 229, 231, 241, 243, 253, 259, 261, 271, 273, 283, 289, 297, 327, 337, 339, 349, 357, 363, 373, 391, 397, 409

Offset: 1

Patrick De Geest, May 15 1998

Obviously there can be no even terms in this sequence. - Alonso del Arte, Jun 18 2017

			Concatenate 4 and 1 to get 41, which is prime, so 1 is in the sequence.
Concatenate 4 and 3 to get 43, which is prime, so 3 is in the sequence.
Concatenate 4 and 5 to get 45 = 3^2 * 5, which is not prime, so 5 is not in the sequence.

Seiichi Manyama, Table of n, a(n) for n = 1..10000 (terms 1..1740 from Vincenzo Librandi)

Cf. other digit 'd' concatenated with a(n) is prime sequences: A032664 (d = 1), A032665 (d = 2), A032666 (d = 3), A032668 (d = 5), A032669 (d = 6), A032670 (d = 7), A032671 (d = 8), A032672 (d = 9), A000040 (d = 0).

Select[2Range[250] - 1, PrimeQ[FromDigits[Join[{4}, IntegerDigits[#]]]] &] (* Alonso del Arte, Jun 18 2017 *)

isok(n) = isprime(eval(concat(4, Str(n)))); \\ Michel Marcus, Jun 19 2017

Offset adjusted at the suggestion of Michel Marcus by Alonso del Arte, Jun 18 2017

A167724 Squares that becomes a prime number when prefixed with a 9.

Original entry on oeis.org

1369, 2401, 2809, 3481, 5929, 9409, 10201, 14161, 16129, 17689, 25921, 28561, 32761, 41209, 44521, 64009, 94249, 100489, 108241, 116281, 117649, 130321, 137641, 146689, 157609, 170569, 175561, 177241, 196249, 201601, 218089, 219961

Offset: 1

Claudio Meller, Nov 10 2009

Subsequence of squares of A032672. - Michel Marcus, Jun 22 2016

G. C. Greubel, Table of n, a(n) for n = 1..10000

Cf. A032672.

Select[Range[1, 500000, 2]^2, PrimeQ[FromDigits[Join[{9}, IntegerDigits[#]]]] &] (* G. C. Greubel, Jun 21 2016 *)

cp's OEIS Frontend

A099678 Numbers n such that 10n01 is a prime.

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A099744 Palindromes n such that 10n01 is a prime.

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Maple

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A032667 Digit '4' concatenated with a(n) is a prime.

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Mathematica

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Extensions

A167724 Squares that becomes a prime number when prefixed with a 9.

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Programs

Mathematica