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.

Showing 1-5 of 5 results.

A034591 Numbers whose concatenation with the next prime yields a prime.

Original entry on oeis.org

0, 2, 6, 8, 9, 12, 27, 31, 36, 42, 44, 45, 51, 56, 63, 68, 69, 78, 83, 86, 93, 94, 96, 98, 102, 104, 105, 108, 115, 117, 118, 123, 126, 132, 138, 150, 151, 154, 156, 157, 160, 167, 176, 180, 183, 186, 192, 194, 195, 199, 201, 205, 213, 217, 219, 225, 230, 233
Offset: 1

Views

Author

Patrick De Geest, Oct 15 1998

Keywords

Examples

			8 is a term because nextprime(8) = 11 and 811 is prime.

Crossrefs

See also A034592, A034593, A034594, A034596, A030459.

Programs

  • Mathematica
    Select[Range[0,250],PrimeQ@FromDigits@Flatten[IntegerDigits/@{#,NextPrime@#}]&] (* Giorgos Kalogeropoulos, Jul 30 2021 *)
  • PARI
    isok(m) = isprime(eval(Str(m, nextprime(m+1)))); \\ Michel Marcus, Oct 03 2014 and Jul 30 2021

A034593 Cycle of 3 steps possible for 'concatenate a(n) and nextprime(a(n)) is a prime'.

Original entry on oeis.org

467, 941, 8834, 9548, 13012, 22302, 23592, 26208, 47538, 58578, 78910, 86447, 86925, 116230, 118040, 123716, 128055, 213493, 234146, 238326, 273057, 285315, 286422, 389336, 399261, 457810, 468764, 481476, 502590, 525402, 541102, 570205
Offset: 0

Views

Author

Patrick De Geest, Oct 15 1998

Keywords

Examples

			a(n)=78910 -> nextprime(a(n)) is 78919 so '7891078919' is prime (=step 1); a(n2)=7891078919 -> nextprime(a(n2)) is 7891078931 so '78910789197891078931' is prime (=step 2); a(n3)=78910789197891078931 -> nextprime(a(n3)) is 78910789197891078949 so '7891078919789107893178910789197891078949' is prime (=step 3).

Crossrefs

See also A034591-A034596, A030459.

A034594 Concatenation of nextprime(a(n)) and a(n) is a prime.

Original entry on oeis.org

3, 27, 33, 39, 47, 51, 53, 61, 63, 91, 111, 123, 129, 131, 143, 173, 189, 199, 211, 217, 219, 231, 233, 237, 257, 273, 279, 301, 319, 341, 353, 357, 417, 423, 429, 473, 481, 489, 493, 501, 519, 523, 529, 531, 537, 551, 561, 573, 579, 587, 597, 607, 609, 619
Offset: 1

Views

Author

Patrick De Geest, Oct 15 1998

Keywords

Examples

			a(n)=27 -> nextprime(a(n)) is 29 so '2927' is a prime.

Links

Crossrefs

See also A034591-A034596, A030459.

Programs

  • PARI
    isok(n)=isprime(fromdigits(concat(digits(nextprime(n+1)), digits(n)))) \\ Andrew Howroyd, Aug 13 2024

Extensions

Offset changed by Andrew Howroyd, Aug 13 2024

A034592 Cycle of 2 steps possible for 'concatenate a(n) and nextprime(a(n)) is a prime'.

Original entry on oeis.org

0, 36, 150, 284, 464, 467, 525, 584, 644, 777, 855, 941, 1058, 1120, 1179, 1362, 1788, 1855, 2368, 2520, 2547, 2550, 2576, 2743, 2988, 3063, 3273, 3339, 3410, 3930, 4054, 4370, 4739, 4843, 4910, 5253, 5445, 5550, 5671, 5967, 6512, 6721, 6987, 7131, 7216
Offset: 0

Views

Author

Patrick De Geest, Oct 15 1998

Keywords

Examples

			a(n)=777 -> nextprime(a(n)) is 787 so '777787' is prime (=step 1); a(n2)=777787 -> nextprime(a(n2)) is 777817 so '777787777817' is prime (=step 2).

Crossrefs

See also A034591-A034596, A030459.

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

Views

Author

Patrick De Geest, Oct 15 1998

Keywords

Examples

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

Links

Crossrefs

Intersection of A034591 and A034594.
Cf. A034596, A034808, A034809, A034814.

Programs

  • Mathematica
    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 *)

Extensions

Offset changed by Andrew Howroyd, Aug 13 2024
Showing 1-5 of 5 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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