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.
d = 72 appears after 31397, while smaller d = 54, 60, 66 come later, following primes 35617, 43331, 162143, respectively.
Module[{nn=32*10^5,prs,gps},prs=Prime[Range[nn]];gps=Differences[prs];Table[SelectFirst[Thread[{Most[prs],gps}],#[[2]]==6n&],{n,30}]][[;;,1]] (* Harvey P. Dale, Mar 03 2025 *)
a(n) = {p=3; q = nextprime(p+1); while((q-p) != 6*n, p = q; q = nextprime(q+1)); p;} \\ Michel Marcus, Mar 12 2016
a(2)=7 because 7 and 11 are consecutive primes with difference 2^2=4. a(3)=89 because 89 and 97 are consecutive primes with difference 2^3=8.
f[n_] := Block[{k = 1}, While[Prime[k + 1] != n + Prime[k], k++ ]; Prime[k]]; Do[ Print[ f[2^n]], {n, 0, 10}] (* Robert G. Wilson v, Jan 13 2005 *)
import sympy
n=0
while n>=0:
p=2
while sympy.nextprime(p)-p!=(2**n):
p=sympy.nextprime(p)
print(p)
n=n+1
p=sympy.nextprime(p)
## Abhiram R Devesh, Aug 09 2014
a(1) = 337, because 337 and 337 + 10 = 347 are two consecutive primes with the same last digit 7 and no smaller prime has this property.
a(n) = my(p=7); while (!isprime(p) || ((nextprime(p+1)-p) != 10*n), p+=10); p; \\ Michel Marcus, Feb 25 2025
from sympy import nextprime, isprime def A381510(n): p = 17 while (q:=nextprime(p)): if q-p == 10*n: return p p = q+9-(q+2)%10 while not isprime(p): p += 10 # Chai Wah Wu, Mar 09 2025
a(1) = 139, because 139 and 139 + 10 = 149 are two consecutive primes with the same last digit 9 and no smaller p has this property.
a(n) = my(p=9); while (!isprime(p) || ((nextprime(p+1)-p) != 10*n), p+=10); p; \\ Michel Marcus, Feb 25 2025
from sympy import isprime, nextprime def A381511(n): p = 19 while (q:=nextprime(p)): if q-p == 10*n: return p p = q+9-(q%10) while not isprime(p): p += 10 # Chai Wah Wu, Mar 08 2025
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