A065840
Numbers n such that the first n quaternary digits found in the base-10 expansion of Pi form a prime (when the decimal point is ignored).
Original entry on oeis.org
1, 2, 3, 5, 10, 19, 72, 115, 220, 315, 375, 12408
Offset: 1
E.g., the first a(5) or 10 quaternary digits of Pi are 31.12332323{4} and 3112332323{4} is the prime 880571{10}.
-
p = First[ RealDigits[ Pi, 10, 10^5]]; p = p[[ Select[ Range[10^5], p[[ # ]] == 0 || p[[ # ]] == 1 || p[[ # ]] == 2 || p[[ # ]] == 3 & ]]]; Do[ If[ PrimeQ[ FromDigits[ Take[p, n], 4]], Print[ n]], {n, 1, 4000} ]
A135697
Palindromes formed from the reflected decimal expansion of Pi.
Original entry on oeis.org
3, 33, 313, 3113, 31413, 314413, 3141413, 31411413, 314151413, 3141551413, 31415951413, 314159951413, 3141592951413, 31415922951413, 314159262951413, 3141592662951413, 31415926562951413, 314159265562951413, 3141592653562951413, 31415926533562951413, 314159265353562951413
Offset: 1
n Digits of a(n)
1 ( 3 )
2 ( 3 3 )
3 ( 3 1 3 )
4 ( 3 1 1 3 )
5 ( 3 1 4 1 3 )
6 ( 3 1 4 4 1 3 )
7 ( 3 1 4 1 4 1 3 )
8 ( 3 1 4 1 1 4 1 3 )
9 ( 3 1 4 1 5 1 4 1 3 )
10 ( 3 1 4 1 5 5 1 4 1 3 )
-
Table[FromDigits[Join[#[[;; Floor[n/2]]], #[[Ceiling[n/2] ;; 1 ;; -1]]]], {n, Length[#]}] & [First[RealDigits[Pi, 10, 25]]] (* Paolo Xausa, Dec 09 2024 *)
A048796
Palindromic primes formed from decimal expansion of Pi written backwards then forwards.
Original entry on oeis.org
3, 131, 32397985356295141314159265358979323
Offset: 1
-
l={};Do[a=Floor[Pi*10^n];r=IntegerReverse[a];r2=Floor[r/10];c=FromDigits[Flatten[IntegerDigits/@Join[r2,a]]];
If[PrimeQ[c],AppendTo[l, c]],{n,0,100}];l (* Metin Sariyar, Jul 07 2020 *)
A135698
Palindromes with odd number of digits formed from the reflected decimal expansion of Pi.
Original entry on oeis.org
3, 313, 31413, 3141413, 314151413, 31415951413, 3141592951413, 314159262951413, 31415926562951413, 3141592653562951413, 314159265353562951413, 31415926535853562951413, 3141592653589853562951413, 314159265358979853562951413, 31415926535897979853562951413
Offset: 1
n ........... a(n)
1 ............ 3
2 ........... 313
3 .......... 31413
4 ......... 3141413
5 ........ 314151413
6 ....... 31415951413
7 ...... 3141592951413
8 ..... 314159262951413
9 .... 31415926562951413
10 .. 3141592653562951413
-
pinxt[n_]:=With[{pid=RealDigits[Pi,10,20][[1]]},Module[{a=Take[pid,n]}, FromDigits[Join[a,Reverse[Most[a]]]]]]; Table[pinxt[n],{n,1,15}] (* Harvey P. Dale, Oct 06 2011 *)
A119351
Indices k of prime palindromic numbers formed by taking k digits in the decimal expansion of Pi and reflecting about the last digit.
Original entry on oeis.org
1, 2, 27, 151, 461, 2056
Offset: 1
Of 3, 313, 31413, 3141413, 314151413, the first and second are primes, so the first two terms are 1 and 2.
- Shyam Sunder Gupta, Mystery of pi, Exploring the Beauty of Fascinating Numbers, Springer (2025) Ch. 19, 473-497.
A065832
Numbers k such that the first k binary digits found in the base-10 expansion of Pi form a prime (when the decimal point is ignored).
Original entry on oeis.org
2, 4, 10, 24, 29, 34, 43, 62, 76, 351, 778, 2736, 4992, 7517, 22044, 40390, 204505
Offset: 1
The first a(3)=10 binary digits of Pi are 1101110001_2 which is prime 881_10.
-
p = First[ RealDigits[ Pi, 10, 10^5]]; p = p[[ Select[ Range[10^5], p[[ # ]] == 0 || p[[ # ]] == 1 & ]]]; Do[ If[ PrimeQ[ FromDigits[ Take[p, n], 2]], Print[n]], {n, 1, Length[p] } ]
Original entry on oeis.org
3, 13, 881, 14436001, 461952047, 14782465513, 7568622343067, 3968137871002260679, 65013970878501038966321
Offset: 1
Original entry on oeis.org
3, 13, 53, 859, 880571, 230836658783, 18727694659923768688081143062632211180505377, 1448985191439414787314128433365601157107793684026416650771108564122239
Offset: 1
A383404
Palindromic primes formed from the reflected decimal expansion of the golden ratio phi.
Original entry on oeis.org
11, 1618033308161, 16180339887498948482045868343656381118365634386854028484989478893308161, 16180339887498948482045868343656381177203030277118365634386854028484989478893308161
Offset: 1
Showing 1-9 of 9 results.
Comments