Original entry on oeis.org
3, 53, 171311753, 8983797371676159534743413731292319171311753
Offset: 1
Micha Fleuren (michafleuren(AT)hotmail.com), Mar 24 2004
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t="";forprime(p=3,9999,ispseudoprime(t=eval(Str(p,t)))&print(t)) \\\\ - M. F. Hasler, Apr 05 2008
Original entry on oeis.org
753, 11753, 1311753, 19171311753, 2319171311753, 292319171311753, 31292319171311753, 3731292319171311753, 413731292319171311753, 43413731292319171311753, 4743413731292319171311753
Offset: 1
Micha Fleuren (michafleuren(AT)hotmail.com), Mar 24 2004
A317903
a(n) = A038394(n)^^A038394(n) (mod 10^len(A038394(n))), where ^^ indicates tetration or hyper-4 (e.g., 3^^4=3^(3^(3^3))).
Original entry on oeis.org
4, 76, 176, 4176, 314176, 91314176, 891314176, 80891314176, 88080891314176, 5288080891314176, 705288080891314176, 10705288080891314176, 2410705288080891314176, 912410705288080891314176, 42912410705288080891314176, 9242912410705288080891314176, 989242912410705288080891314176
Offset: 1
For n = 6, a(6) = 13117532^^13117532 (mod 10^8) == 91314176.
- Marco Ripà, La strana coda della serie n^n^...^n, Trento, UNI Service, Nov 2011, page 60. ISBN 978-88-6178-789-6
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tmod(b, n) = {if (b % n == 0, return (0)); if (b % n == 1, return (1)); if (gcd(b, n)==1, return (lift(Mod(b, n)^tmod(b, lift(znorder(Mod(b, n))))))); lift(Mod(b, n)^(eulerphi(n) + tmod(b, eulerphi(n))));}
f(n) = fromdigits(concat([digits(p) | p<-Vecrev(primes(n))])); \\ A038394
a(n) = if (n==1, 4, my(x=f(n)); tmod(x, 10^#Str(x))); \\ Michel Marcus, Sep 12 2021
A100003
Prime numbers p such that the concatenation of all odd primes up through p in decreasing order is prime.
Original entry on oeis.org
3, 5, 17, 89, 383, 8831
Offset: 1
17 is in the sequence because 17.13.11.7.5.3 is prime (dot between numbers means concatenation).
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Do[If[PrimeQ[(v={};Do[v=Join[v, IntegerDigits[Prime[n-j+1]]], {j, n-1}];FromDigits[v])], Print[Prime[n]]], {n, 2, 4413}]
Prime[#]&/@Select[Range[100],PrimeQ[FromDigits[Flatten[IntegerDigits/@ Prime[Range[#,2,-1]]]]]&] (* To generate a(6) increase the Range by 1000, but the program will run a long time. *) (* Harvey P. Dale, Nov 27 2015 *)
A086043
Concatenation of first n twin primes.
Original entry on oeis.org
3, 35, 357, 35711, 3571113, 357111317, 35711131719, 3571113171929, 357111317192931, 35711131719293141, 3571113171929314143, 357111317192931414359, 35711131719293141435961, 3571113171929314143596171, 357111317192931414359617173, 357111317192931414359617173101
Offset: 1
-
Primes:= select(isprime, {seq(i,i=1..100,2)}):
T1:= Primes intersect map(`+`,Primes,2):
Twins:= sort(convert(T1 union map(`-`,T1,2),list)):
dcat:= (a,b) -> a*10^(1+ilog10(b))+b:
A[1]:= 3:
for n from 2 to nops(Twins) do A[n]:= dcat(A[n-1],Twins[n]) od:
seq(A[i],i=1..nops(Twins)); # Robert Israel, Sep 01 2016
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Table[FromDigits@ Flatten@ Map[IntegerDigits, Take[#, n]], {n, Length@ #}] &[Union@ Join[#, # + 2] &@ Select[Prime@ Range@ 17, NextPrime@ # - 2 == # &]] (* Michael De Vlieger, Sep 01 2016 *)
Module[{tps=Union[Flatten[Select[Partition[Prime[Range[50]],2,1],#[[2]]-#[[1]] == 2&]]]},FromDigits[Flatten[IntegerDigits/@#]]&/@Table[Take[tps,n],{n,Length[tps]}]] (* Harvey P. Dale, Jun 16 2022 *)
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concattwprb(n) = { y=3; forprime(x=5,n, if(isprime(x+2) || isprime(x-2), y=eval(concat(Str(y),Str(x))); print1(y",") ) ) }
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