A032702 -id:A032702 - cp's OEIS frontend

A032708 Numbers k such that k prefixed by '8' and followed by '1' is prime.

1, 2, 8, 10, 11, 16, 17, 19, 22, 23, 29, 31, 43, 46, 50, 52, 58, 64, 68, 73, 74, 76, 82, 83, 86, 94, 95, 97, 100, 103, 104, 107, 110, 113, 118, 128, 133, 137, 140, 142, 155, 161, 167, 170, 176, 190, 193, 197, 202, 203, 205, 214, 217, 223, 224, 226, 230, 235

Offset: 1

Patrick De Geest, May 15 1998

Cf. A032702-A032733.

Select[Range[250],PrimeQ[FromDigits[Join[{8}, IntegerDigits[#],{1}]]]&]  (* Harvey P. Dale, Mar 24 2011 *)

Offset changed by Andrew Howroyd, Aug 11 2024

A032709 Numbers k such that k prefixed by '9' and followed by '1' is prime.

Original entry on oeis.org

1, 4, 7, 9, 15, 16, 18, 22, 24, 28, 31, 34, 37, 39, 42, 43, 46, 49, 51, 52, 55, 60, 63, 66, 72, 78, 79, 81, 85, 87, 90, 93, 94, 108, 112, 114, 115, 129, 133, 138, 141, 154, 157, 159, 162, 163, 169, 171, 177, 178, 180, 181, 184, 192, 195, 196, 204, 205, 211, 222

Offset: 1

Patrick De Geest, May 15 1998

Cf. A032702-A032733.

Offset changed by Andrew Howroyd, Aug 13 2024

A032712 Numbers k such that k prefixed by '4' and followed by '3' is prime.

Original entry on oeis.org

3, 4, 6, 13, 15, 24, 25, 27, 28, 36, 37, 42, 46, 48, 49, 51, 52, 58, 60, 64, 66, 67, 70, 72, 73, 78, 79, 81, 90, 93, 94, 97, 99, 102, 111, 114, 118, 120, 121, 123, 124, 126, 133, 141, 144, 145, 151, 154, 159, 160, 181, 184, 186, 189, 190, 195, 198, 201, 202

Offset: 1

Patrick De Geest, May 15 1998

Cf. A032702-A032733.

Offset changed by Andrew Howroyd, Aug 13 2024

A032718 Numbers k such that k prefixed by '1' and followed by '7' is prime.

Original entry on oeis.org

0, 2, 3, 5, 6, 9, 11, 18, 21, 23, 27, 29, 30, 32, 36, 42, 44, 48, 56, 59, 60, 62, 63, 65, 66, 69, 74, 77, 78, 84, 86, 87, 90, 98, 99, 102, 104, 105, 108, 111, 117, 119, 125, 128, 131, 143, 144, 146, 149, 152, 158, 159, 161, 165, 167, 171, 177, 180, 182, 186

Offset: 1

Patrick De Geest, May 15 1998

Cf. A032702-A032733.

Offset changed by Andrew Howroyd, Aug 13 2024

A032722 Numbers k such that k prefixed by '5' and followed by '7' is prime.

Original entry on oeis.org

4, 5, 7, 8, 10, 14, 16, 19, 22, 23, 29, 34, 38, 40, 41, 43, 47, 50, 52, 55, 64, 65, 71, 73, 80, 82, 85, 86, 89, 92, 98, 104, 113, 115, 119, 121, 125, 128, 130, 134, 140, 142, 143, 148, 151, 157, 160, 163, 164, 176, 178, 179, 181, 182, 190, 197, 202, 205, 206, 212

Offset: 1

Patrick De Geest, May 15 1998

Cf. A032702-A032733.

Select[Range[250],PrimeQ[FromDigits[Join[{5},IntegerDigits[#], {7}]]]&] (* Harvey P. Dale, Jul 24 2011 *)

Offset changed by Andrew Howroyd, Aug 13 2024

A032730 Numbers k such that k prefixed by '5' and followed by '9' is prime.

Original entry on oeis.org

0, 6, 9, 11, 17, 18, 20, 27, 30, 39, 41, 44, 47, 51, 56, 63, 65, 66, 68, 74, 77, 83, 84, 86, 87, 93, 105, 110, 116, 119, 122, 123, 132, 134, 141, 143, 144, 147, 153, 159, 165, 167, 171, 174, 176, 182, 183, 185, 186, 189, 192, 194, 200, 206, 218, 224, 225

Offset: 1

Patrick De Geest, May 15 1998

Cf. A032702-A032733.

Select[Range[0,250],PrimeQ[FromDigits[Join[{5},IntegerDigits[#], {9}]]]&] (* Harvey P. Dale, May 09 2011 *)

Offset changed by Andrew Howroyd, Aug 13 2024

A032736 a(n) cannot be prefixed or followed by any digit to form a prime ('empty' prefixes allowed).

Original entry on oeis.org

14612, 27971, 29289, 33170, 36186, 38327, 39608, 40078, 41165, 41528, 43277, 44657, 47382, 55553, 55791, 58899, 60806, 62318, 63056, 65970, 66818, 70558, 73851, 80477, 81167, 83986, 86145, 89072, 89280, 90379, 91538, 93160, 96222

Offset: 1

Patrick De Geest, May 15 1998

			60806 prefixed with a digit from ('',1,2,3,4,5,6,7,8,9) and followed by a digit from (1,3,7,9) never yields a prime: '_'60806'3' = 43 x 79 x 179; '1'14612'3' = 3^3 x 11 x 17 x 227.

Cf. A032682-A032685 and A032702-A032733.

Offset changed by Andrew Howroyd, Aug 13 2024

A032738 a(n) cannot be prefixed or followed by any digit to form a prime ('empty' prefixes and suffixes are allowed).

Original entry on oeis.org

14612, 27971, 33170, 36186, 39608, 40078, 41165, 41528, 47382, 55553, 60806, 62318, 63056, 65970, 66818, 70558, 83986, 86145, 89072, 89280, 91538, 93160, 96222, 97908, 101532, 102852, 104609, 105275, 108312, 108615, 108792, 109934

Offset: 1

Patrick De Geest, May 15 1998

a(n) itself cannot be a prime to start with.

			104609 prefixed or followed by a digit from ('',1,2,3,4,5,6,7,8,9) never yields a prime: '_'104609'_' = 73 x 1433; '8'104609'3' = 3089 x 26237.

Cf. A032682-A032685 and A032702-A032733.

Offset changed by Andrew Howroyd, Aug 13 2024

A084429 Integers m such that the base-10 digit concatenation 4//m//3//m//2//m//1 is prime.

Original entry on oeis.org

14, 15, 23, 25, 37, 39, 44, 54, 55, 70, 79, 88, 90, 98, 102, 118, 123, 134, 136, 143, 144, 151, 174, 182, 202, 209, 215, 226, 230, 232, 245, 254, 256, 257, 258, 262, 264, 267, 272, 284, 287, 297, 300

Offset: 1

Farideh Firoozbakht, Jun 27 2003

I called this sequence f4i and defined similar sequences {fni} in the comments in A083660: fni(m) is the m-th nonnegative integer k such that the concatenation fi(n, k) = n//k//n-1//k// ...//3//k//2//k//1 is prime. By this definition f2i = A032702.

			a(3)=23 because 23 is the third nonnegative integer m such that fi(4,m) = fi(4,23) = 4 // 23 // 3 // 23 // 2 // 23 // 1 = 4233232231 is prime.

Cf. A083660, A032702.

Do[If[PrimeQ[FromDigits[Join[{4}, IntegerDigits[n], {3}, IntegerDigits[n], {2}, IntegerDigits[n], {1}]]], v=Insert[v, n, -1]], {n, 300}]; v

cp's OEIS Frontend

A032708 Numbers k such that k prefixed by '8' and followed by '1' is prime.

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A032709 Numbers k such that k prefixed by '9' and followed by '1' is prime.

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A032712 Numbers k such that k prefixed by '4' and followed by '3' is prime.

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A032718 Numbers k such that k prefixed by '1' and followed by '7' is prime.

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A032722 Numbers k such that k prefixed by '5' and followed by '7' is prime.

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A032730 Numbers k such that k prefixed by '5' and followed by '9' is prime.

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A032736 a(n) cannot be prefixed or followed by any digit to form a prime ('empty' prefixes allowed).

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A032738 a(n) cannot be prefixed or followed by any digit to form a prime ('empty' prefixes and suffixes are allowed).

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A084429 Integers m such that the base-10 digit concatenation 4//m//3//m//2//m//1 is prime.

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Mathematica