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 1-6 of 6 results.

A072367 Squares x such that x + reverse of x is a prime.

Original entry on oeis.org

1, 100, 196, 625, 10816, 13456, 15376, 18496, 21025, 22201, 22801, 24649, 25921, 27889, 29929, 33856, 35344, 36100, 42025, 50176, 60025, 63001, 70756, 71824, 73984, 78400, 82369, 83521, 96100, 1012036, 1048576, 1073296, 1123600, 1144900
Offset: 1

Views

Author

Shyam Sunder Gupta, Jul 18 2002

Keywords

Examples

			196 is a term because 196 is a square and 196+691=887 is a prime.

Links

Crossrefs

Cf. A056964, A072366.

Programs

  • Magma
    [k:k in [m^2:m in [1..1100]]| IsPrime(Seqint(Intseq(k,10))+Seqint(Reverse(Intseq(k,10))))]; // Marius A. Burtea, Jun 20 2019
  • Maple
    select(t -> isprime(t+revdigs(t)), [seq(i^2,i=1..10000)]); # Robert Israel, Jun 19 2019
  • Mathematica
    Select[Range[1100]^2,PrimeQ[#+FromDigits[Reverse[IntegerDigits[#]]]]&]  (* Harvey P. Dale, Feb 20 2011 *)
  • PARI
    isok(x) = issquare(x) && isprime(x+fromdigits(Vecrev(digits(x)))); \\ Michel Marcus, Jun 19 2019

A072369 Cubes x such that x + reverse of x is a prime.

Original entry on oeis.org

1, 512, 17576, 39304, 42875, 1643032, 1815848, 2352637, 2685619, 3511808, 4826809, 6331625, 7529536, 9528128, 125000000, 153990656, 155720872, 175616000, 181321496, 183250432, 208527857, 265847707, 281011375, 306182024, 308915776, 334255384, 357911000, 403583419
Offset: 1

Views

Author

Shyam Sunder Gupta, Jul 18 2002

Keywords

Examples

			512 is a term because 512 = 9^3 is a cube and 512 + 215 = 727 is a prime.

Links

Crossrefs

Cf. A000578, A056964, A072366.

Programs

  • Mathematica
    Select[Range[1000], PrimeQ[#^3 + FromDigits @ Reverse @ IntegerDigits[#^3]] &]^3 (* Amiram Eldar, Aug 24 2020 *)
Select[Range[1000]^3,PrimeQ[#+IntegerReverse[#]]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Oct 18 2020 *)

Extensions

More terms from Amiram Eldar, Aug 24 2020

A072387 Triangular number x such that x + reverse of x is a prime.

Original entry on oeis.org

1, 10, 190, 11026, 11476, 12880, 13366, 19306, 21115, 23005, 26335, 28441, 36046, 53956, 54946, 58996, 60031, 65341, 68635, 70876, 72010, 83845, 91378, 1030330, 1047628, 1095940, 1100386, 1154440, 1205128, 1209790, 1223830, 1242676, 1247410, 1266436, 1285606
Offset: 1

Views

Author

Shyam Sunder Gupta, Jul 20 2002

Keywords

Examples

			10 is a term because it is a triangular number and 10 + 01 = 11 is a prime.

Links

Crossrefs

Intersection of A000217 and A072366. - Michel Marcus, Nov 29 2014
Cf. A056964.

Programs

  • Mathematica
    tri[n_] := n*(n + 1)/2; tri /@ Select[Range[10^3], PrimeQ[(t = tri[#]) + FromDigits @ Reverse @ IntegerDigits[t]] &] (* Amiram Eldar, Aug 24 2020 *)
Select[Accumulate[Range[2000]],PrimeQ[#+IntegerReverse[#]]&] (* Harvey P. Dale, Nov 27 2021 *)
  • PARI
    isok(n) = ispolygonal(n, 3) && isprime(n+subst(Polrev(digits(n)), x, 10)); \\ Michel Marcus, Nov 29 2014

Extensions

More terms from Michel Marcus, Nov 29 2014

A130864 Numbers x such that x + reverse of x is a non-palindromic prime.

Original entry on oeis.org

158, 166, 170, 172, 178, 182, 188, 190, 196, 229, 239, 257, 265, 269, 271, 277, 281, 287, 295, 299, 328, 338, 356, 364, 368, 370, 376, 380, 386, 394, 398, 427, 437, 439, 455, 463, 467, 469, 475, 479, 485, 493, 497, 499, 526, 536, 538, 554, 562, 566, 568
Offset: 0

Views

Author

Tanya Khovanova, Jul 23 2007

Keywords

Links

Crossrefs

A subsequence of A072366 = Numbers x such that x + reverse of x is a prime.

Programs

  • Mathematica
    Select[Range[1000], PrimeQ[ # + FromDigits[Reverse[IntegerDigits[ # ]]]] && # + FromDigits[Reverse[IntegerDigits[ # ]]] != FromDigits[ Reverse[IntegerDigits[ # + FromDigits[Reverse[IntegerDigits[ # ]]]]]] &]
nppQ[n_]:=With[{c=n+IntegerReverse[n]},PrimeQ[c]&&!PalindromeQ[c]]; Select[ Range[600],nppQ] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jan 27 2021 *)

A177948 Numbers n such that n^2 + reverse of n^2 is a prime.

Original entry on oeis.org

1, 10, 14, 25, 104, 116, 124, 136, 145, 149, 151, 157, 161, 167, 173, 184, 188, 190, 205, 224, 245, 251, 266, 268, 272, 280, 287, 289, 310, 1006, 1024, 1036, 1060, 1070, 1124, 1150, 1216, 1220, 1240, 1244, 1250, 1286, 1306, 1310, 1336, 1366, 1376, 1406, 1417
Offset: 1

Views

Author

Michel Lagneau, May 15 2010

Keywords

Examples

			116 is in the sequence, because 116^2 = 13456, and 13456 + 65431 = 78887 is a prime.

Crossrefs

Cf. A000040, A072366.

Programs

  • Mathematica
    Select[Range[2000], PrimeQ[(#)^2 + FromDigits[Reverse[IntegerDigits[(#)^2]]]] &]

A371508 Integers k such that A000045(k) + A004091(k) is prime (A000040).

Original entry on oeis.org

1, 2, 81, 311, 6887, 9691, 296959
Offset: 1

Views

Author

Gonzalo Martínez, Mar 25 2024

Keywords

Examples

			1 is a term since Fibonacci(1) = 1 plus its reversal is 1 + 1 = 2 which is prime (and for the same reason 2 is a term).
81 is a term since Fibonacci(81) = 37889062373143906 plus its reversal is 98823199699242779 which is prime.

Crossrefs

Cf. A000040, A000045, A004091, A072366.

Programs

  • Mathematica
    Select[Range[10^4], PrimeQ[(f = Fibonacci[#]) + IntegerReverse[f]] &] (* Amiram Eldar, Mar 25 2024 *)

Extensions

a(7) from Michael S. Branicky, Jan 07 2025
Showing 1-6 of 6 results.

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

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