A014208 -id:A014208 - cp's OEIS frontend

A186698 Next prime after n-th positive palindrome.

2, 3, 5, 5, 7, 7, 11, 11, 11, 13, 23, 37, 47, 59, 67, 79, 89, 101, 103, 113, 127, 137, 149, 157, 163, 173, 191, 193, 211, 223, 223, 233, 251, 257, 263, 277, 283, 293, 307, 317, 331, 337, 347, 359, 367, 379, 389, 397, 409, 419, 431, 439, 449, 457, 467, 479, 487, 499, 509, 521, 541, 541, 547, 557, 569, 577, 587, 599, 607, 617, 631, 641, 647

Offset: 1

Harvey P. Dale, Feb 25 2011

There are infinitely many n for which a(n+1) = a(n). For example, when 10^k + 1 is composite, 10^k - 1 and 10^k + 1 are successive palindromes which have the same next prime. - Robert Israel, Nov 04 2015

Chai Wah Wu, Table of n, a(n) for n = 1..10000

Cf. A014208, A186697, A151800, A002113.

digrev:= proc(x) option remember; local t;
   t:= x mod 10;
   t*10^ilog10(x)+procname((x-t)/10)
end proc:
for x from 0 to 9 do digrev(x):= x od:
N:=6;
Pals:= $1..9:
for d from 2 to N do
  if d::even then
    m:= d/2;
    Pals:= Pals, seq(n*10^m + digrev(n), n=10^(m-1)..10^m-1);
  else
    m:= (d-1)/2;
    Pals:= Pals, seq(seq(n*10^(m+1)+y*10^m+digrev(n), y=0..9), n=10^(m-1)..10^m-1);
  fi
od:
Pals:=[Pals]:
map(nextprime,Pals); # Robert Israel, Nov 04 2015

NextPrime[Select[Range[700],PalindromeQ]] (* Harvey P. Dale, Jan 31 2024 *)

from sympy import nextprime
def A186698(n): return int(nextprime((c:=n+1-x)*x+int(str(c)[-2::-1] or 0) if n+1<(x:=10**(len(str(n+1>>1))-1))+(y:=10*x) else (c:=n+1-y)*y+int(str(c)[::-1] or 0))) # Chai Wah Wu, Jul 10 2024

a(n) = A151800(A002113(n+1)). - Michael S. Branicky, Jul 10 2024

A182487 Nextprime(F(n)) - prevprime(F(n)), where F(n) is the n-th Fibonacci number.

Original entry on oeis.org

3, 4, 4, 6, 4, 6, 6, 14, 10, 10, 6, 6, 8, 18, 12, 24, 16, 10, 6, 12, 30, 12, 24, 42, 30, 24, 60, 24, 30, 34, 30, 36, 46, 12, 36, 18, 34, 24, 24, 30, 36, 52, 72, 16, 22, 48, 44, 50, 34, 20, 20, 28, 44, 50, 40, 92, 60, 86, 16, 52, 48, 66, 46, 168, 50, 174, 36

Offset: 4

Alex Ratushnyak, May 02 2012

Smallest prime following Fibonacci(n) minus largest prime immediately preceding Fibonacci(n). Starting from Fibonacci(4), because for n<4 there is no prime preceding Fibonacci(n).

			a(0) = A014208(4) - A180422(0) = 5 - 2 = 3,
a(7) = A014208(11) - A180422(7) = 97-83 = 14.

Alois P. Heinz, Table of n, a(n) for n = 4..1000

Cf. A014208, A180422, A013633, A058043, A058054, A161503.

Cf. A079677 (distance from F(n) to the nearest prime).

a:= n-> (f-> nextprime(f)-prevprime(f))(combinat[fibonacci](n)):
seq(a(n), n=4..100);  # Alois P. Heinz, Jul 29 2015

Table[f = Fibonacci[n]; NextPrime[f] - NextPrime[f, -1], {n, 4, 100}] (* T. D. Noe, May 02 2012 *)

a(n) = A014208(n+4) - A180422(n).

A186697 Next Fibonacci number after n-th prime number.

Original entry on oeis.org

3, 5, 8, 8, 13, 21, 21, 21, 34, 34, 34, 55, 55, 55, 55, 55, 89, 89, 89, 89, 89, 89, 89, 144, 144, 144, 144, 144, 144, 144, 144, 144, 144, 144, 233, 233, 233, 233, 233, 233, 233, 233, 233, 233, 233, 233, 233, 233, 233, 233, 377, 377, 377, 377, 377, 377, 377, 377, 377, 377, 377, 377, 377, 377, 377, 377, 377, 377, 377, 377, 377, 377, 377, 377, 610

Offset: 1

Harvey P. Dale, Feb 25 2011

nonn

Cf. A014208 (next prime after the n-th Fibonacci number).

With[{fibs=Fibonacci[Range[20]]},Table[First[Select[fibs,#>Prime[n]&]],{n,75}]]

A186700 Next palindrome after n-th prime.

Original entry on oeis.org

3, 4, 6, 8, 22, 22, 22, 22, 33, 33, 33, 44, 44, 44, 55, 55, 66, 66, 77, 77, 77, 88, 88, 99, 99, 111, 111, 111, 111, 121, 131, 141, 141, 141, 151, 161, 161, 171, 171, 181, 181, 191, 202, 202, 202, 202, 212, 232, 232, 232, 242, 242, 242, 252, 262, 272, 272, 272, 282, 282, 292, 303, 313, 313, 323, 323, 333, 343, 353, 353, 363, 363, 373, 383, 383, 393, 393, 404, 404

Offset: 1

Harvey P. Dale, Feb 25 2011

Chai Wah Wu, Table of n, a(n) for n = 1..10000

Cf. A014208, A186698.

palQ[n_] := # == Reverse@ # &@ IntegerDigits@ n; Table[k = Prime@ n + 1; While[! palQ@ k, k++]; k, {n, 79}] (* Michael De Vlieger, Nov 05 2015 *)

a(n) = {p = prime(n)+1; while ((d = digits(p)) && (Vecrev(d)!=d), p++); p;} \\ Michel Marcus, Nov 05 2015

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A186698 Next prime after n-th positive palindrome.

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A182487 Nextprime(F(n)) - prevprime(F(n)), where F(n) is the n-th Fibonacci number.

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A186697 Next Fibonacci number after n-th prime number.

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A186700 Next palindrome after n-th prime.

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