cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A032714 Numbers k such that k prefixed by '6' and followed by '3' is prime.

Original entry on oeis.org

1, 4, 5, 7, 8, 11, 13, 14, 16, 17, 20, 26, 32, 34, 35, 37, 47, 55, 56, 65, 67, 70, 73, 76, 79, 80, 82, 83, 86, 88, 98, 104, 115, 122, 125, 128, 133, 134, 136, 140, 146, 148, 149, 154, 155, 158, 160, 161, 164, 167, 170, 172, 181, 184, 193, 200, 205, 214, 221
Offset: 1

Views

Author

Patrick De Geest, May 15 1998

Keywords

Links

Crossrefs

Cf. A032702-A032733.

Programs

  • Mathematica
    Select[Range[300],PrimeQ[FromDigits[Join[{6},IntegerDigits[#],{3}]]]&] (* Harvey P. Dale, Mar 09 2013 *)

Extensions

Offset changed by Andrew Howroyd, Aug 13 2024

A032715 Numbers k such that k prefixed by '7' and followed by '3' is prime.

Original entry on oeis.org

3, 4, 7, 10, 19, 21, 24, 25, 28, 33, 39, 43, 52, 57, 58, 60, 64, 67, 70, 72, 75, 79, 82, 85, 87, 88, 93, 96, 99, 102, 114, 115, 123, 126, 129, 133, 135, 136, 141, 144, 145, 147, 148, 150, 156, 159, 163, 166, 169, 171, 184, 193, 196, 198, 199, 204, 205, 207
Offset: 1

Views

Author

Patrick De Geest, May 15 1998

Keywords

Links

Crossrefs

Cf. A032702-A032733.

Programs

  • Mathematica
    Select[Range[300],PrimeQ[FromDigits[Join[{7},IntegerDigits[#],{3}]]]&] (* Harvey P. Dale, Mar 31 2024 *)

Extensions

Offset changed by Andrew Howroyd, Aug 13 2024

A032717 Numbers k such that k prefixed by '9' and followed by '3' is prime.

Original entry on oeis.org

5, 8, 10, 13, 17, 20, 28, 29, 32, 34, 40, 41, 43, 46, 47, 53, 61, 62, 64, 73, 74, 80, 83, 88, 92, 97, 103, 115, 116, 118, 119, 124, 125, 128, 130, 137, 139, 142, 143, 145, 146, 149, 151, 157, 158, 167, 170, 173, 175, 181, 182, 187, 194, 200, 203, 208, 214
Offset: 1

Views

Author

Patrick De Geest, May 15 1998

Keywords

Examples

			953 is prime, so 5 is a term.

Links

Crossrefs

Cf. A032702-A032733.

Programs

  • Mathematica
    Select[Range[250],PrimeQ[FromDigits[Join[{9},IntegerDigits[#],{3}]]]&] (* Harvey P. Dale, Jul 30 2013 *)

Extensions

Offset corrected by Matthew House, Jan 15 2017

A032721 Numbers k such that k prefixed by '4' and followed by '7' is prime.

Original entry on oeis.org

5, 6, 8, 12, 15, 17, 21, 29, 32, 33, 35, 39, 44, 45, 50, 51, 54, 56, 59, 63, 65, 78, 81, 87, 93, 95, 96, 98, 101, 104, 105, 107, 111, 117, 122, 125, 135, 138, 146, 150, 159, 161, 162, 164, 168, 173, 177, 188, 189, 192, 194, 195, 201, 215, 218, 219, 222, 225
Offset: 1

Views

Author

Patrick De Geest, May 15 1998

Keywords

Links

Crossrefs

Cf. A032702-A032733.

Programs

  • Mathematica
    Select[Range[300],PrimeQ[FromDigits[Join[{4},IntegerDigits[#],{7}]]]&] (* Harvey P. Dale, Jan 08 2019 *)

Extensions

Offset changed by Andrew Howroyd, Aug 13 2024

A032725 Numbers k such that k prefixed by '9' and followed by '7' is prime.

Original entry on oeis.org

0, 3, 4, 6, 7, 9, 12, 13, 15, 18, 22, 25, 27, 33, 37, 39, 43, 46, 49, 54, 58, 67, 69, 76, 78, 81, 85, 88, 90, 96, 109, 112, 123, 129, 136, 138, 139, 145, 157, 175, 180, 183, 186, 195, 196, 199, 207, 210, 217, 222, 223, 229, 231, 234, 235, 237, 238, 246, 250, 255
Offset: 1

Views

Author

Patrick De Geest, May 15 1998

Keywords

Links

Crossrefs

Cf. A032702-A032733.

Programs

  • Mathematica
    Select[Range[0,300],PrimeQ[FromDigits[Join[{9},IntegerDigits[#],{7}]]]&] (* Harvey P. Dale, Mar 01 2025 *)

Extensions

Offset changed by Andrew Howroyd, Aug 13 2024

A032727 Numbers k such that k prefixed by '2' and followed by '9' is prime.

Original entry on oeis.org

2, 3, 6, 12, 17, 23, 26, 30, 33, 38, 39, 45, 53, 54, 57, 60, 65, 68, 69, 71, 72, 74, 78, 81, 87, 90, 93, 96, 99, 101, 105, 108, 113, 114, 116, 117, 126, 131, 137, 141, 149, 152, 155, 156, 158, 159, 164, 173, 179, 183, 185, 192, 203, 207, 210, 212, 215, 218, 222
Offset: 1

Views

Author

Patrick De Geest, May 15 1998

Keywords

Links

Crossrefs

Cf. A032702-A032733.

Programs

  • Mathematica
    Select[Range[300],PrimeQ[FromDigits[Join[{2},IntegerDigits[#],{9}]]]&] (* Harvey P. Dale, Apr 02 2017 *)

A032728 Numbers k such that k prefixed by '3' and followed by '9' is prime.

Original entry on oeis.org

4, 5, 7, 8, 10, 11, 16, 20, 22, 25, 29, 31, 32, 35, 38, 44, 46, 49, 52, 53, 55, 65, 70, 71, 73, 76, 77, 88, 91, 92, 98, 101, 103, 106, 107, 113, 115, 118, 121, 124, 125, 131, 137, 146, 148, 164, 169, 172, 176, 179, 184, 185, 200, 202, 205, 206, 208, 209, 211
Offset: 1

Views

Author

Patrick De Geest, May 15 1998

Keywords

Links

Crossrefs

Cf. A032702-A032733.

Programs

  • Mathematica
    Select[Range[250],PrimeQ[FromDigits[Join[{3},IntegerDigits[#],{9}]]]&] (* Harvey P. Dale, Aug 17 2021 *)

Extensions

Offset changed by Andrew Howroyd, Aug 13 2024

A032729 Numbers k such that k prefixed by '4' and followed by '9' is prime.

Original entry on oeis.org

0, 1, 3, 4, 7, 9, 12, 13, 15, 21, 22, 25, 28, 33, 34, 40, 51, 54, 63, 64, 67, 72, 75, 78, 79, 88, 90, 91, 96, 99, 103, 114, 117, 118, 126, 129, 138, 139, 147, 151, 153, 154, 157, 160, 165, 166, 171, 172, 175, 180, 184, 187, 195, 196, 199, 201, 208, 213, 216
Offset: 1

Views

Author

Patrick De Geest, May 15 1998

Keywords

Links

Crossrefs

Cf. A032702-A032733.

Programs

  • Mathematica
    Select[Range[0,300],PrimeQ[FromDigits[Join[{4},IntegerDigits[#],{9}]]]&] (* Harvey P. Dale, Jun 04 2019 *)

A032735 Palindromes that cannot be prefixed and followed by any digit to form a prime.

Original entry on oeis.org

11111, 60806, 65356, 1115111, 1392931, 1643461, 1762671, 1797971, 1799971, 1863681, 1911191, 2005002, 2190912, 2429242, 2499942, 2512152, 2708072, 2714172, 2794972, 2845482, 2848482, 2942492, 2993992, 3150513, 3239323
Offset: 1

Views

Author

Patrick De Geest, May 15 1998

Keywords

Examples

			11111 prefixed and followed with a digit from (1,2,3,4,5,6,7,8,9) never yields a prime: '2'11111'3' = 29 x 72797.

Links

Crossrefs

Cf. A032682-A032685 and A032702-A032733.

A083660 Smallest nonnegative integer m such that the concatenation of the integers from n to 1 interspersed with those of m, in base 10, is prime.

Original entry on oeis.org

1, 5, 14, 5, 5, 9, 1, 1, 29, 23, 28, 13, 46, 22, 18, 116, 35, 18, 155, 7, 81, 1, 139, 52, 262, 215, 56, 29, 11, 6, 256, 119, 381, 592, 67, 189, 116, 46, 5, 275, 139, 27, 101, 118, 96, 167, 196, 393, 275, 91, 146, 415, 193, 127, 85, 73, 6, 4, 50, 118, 1046, 362, 5, 431, 248, 180, 82, 230, 125
Offset: 2

Views

Author

Farideh Firoozbakht, Jun 14 2003

Keywords

Comments

Firoozbakht's conjecture: there exists an a(n) for every n greater than 1 and it is less than n^2.
For n with one digit, the searched-for prime must have at least 2n - 1 digits in base 10.
Firoozbakht's conjecture holds true up to at least 100. With adequately coded commands, verification should not take longer than a minute. - Alonso del Arte, Dec 09 2009

Examples

			a(4) = 14 because the concatenation of the digits from 4 to 1 (that is, 4321) with 14 stuck between each of them is 4143142141, and that is a prime number. Similar concatenations with numbers less than 14 used in 14's place all give composite numbers.

Links

  • C. Rivera, Puzzle 8 (www.primepuzzles.net).

Crossrefs

Cf. A032702.

Programs

  • Mathematica
    (*In the absence of a base argument, the function leastGenPrimeByListingFNI assumes the base is 10. Minimum and maximum allowed base values are 2 and 36.*) leastGenPrimeByListingFNI[n_, b_: 10] := Module[{m = 0, p, flag = False}, While[Not[flag], m++; p = FromDigits[Flatten[{Table[{IntegerDigits[i, b], IntegerDigits[m, b]}, {i, n, 2, -1}], {1}}], b]; flag = PrimeQ[p]]; Return[m]]; Table[leastGenPrimeByListingFNI[n], {n, 2, 10}]

Extensions

Terms verified by Alonso del Arte, Dec 09 2009
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