A048398 -id:A048398 - cp's OEIS frontend

A048404 Primes with consecutive digits that differ exactly by 7.

2, 3, 5, 7, 29, 181, 929, 18181, 929292929, 18181818181818181818181818181818181818181818181818181818181818181818181818181

Offset: 1

Patrick De Geest, Apr 15 1999

The next term (a(11)) has 163 digits. - Harvey P. Dale, Mar 23 2023

Sean A. Irvine, Table of n, a(n) for n = 1..13

Cf. A048398, A048399, A048400, A048401, A048402, A048403, A048405, A048409.

Module[{s18,s81,s29,s92},s18=Select[Table[FromDigits[PadRight[{},n,{1,8}]],{n,1,181,2}],PrimeQ]; s81=Select[Table[FromDigits[PadRight[{},n,{8,1}]],{n,2,182,2}],PrimeQ];s29 = Select[ Table[FromDigits[PadRight[{},n,{2,9}]],{n,2,182,2}],PrimeQ]; s92 =Select[Table[ FromDigits[ PadRight[{},n,{9,2}]],{n,1,183,2}],PrimeQ]; Join[{2,3,5,7},s18,s81,s29,s92]//Sort] (* Harvey P. Dale, Mar 23 2023 *)

A048403 Primes with consecutive digits that differ exactly by 6.

Original entry on oeis.org

2, 3, 5, 7, 17, 71, 1717171717171717171717171717171, 1717171717171717171717171717171717171

Offset: 1

Patrick De Geest, Apr 15 1999

From Andrew Howroyd, Aug 13 2024: (Start)
Terms with more than 1 digit have digits alternating between 1 and 7.
No more terms < 10^3000. (End)

Primes in A048408.

Cf. A048398, A048399, A048400, A048401, A048402, A048404, A048405.

upto(limit)={my(L=List([t|t<-[2,3,5],t<=limit]),m=1); while(mAndrew Howroyd, Aug 13 2024

Offset changed by Andrew Howroyd, Aug 13 2024

A052017 Primes with digits in ascending order that differ exactly by 1.

Original entry on oeis.org

2, 3, 5, 7, 23, 67, 89, 4567, 23456789

Offset: 1

Patrick De Geest, Nov 15 1999

Primes in A138141. - Omar E. Pol, Dec 07 2008

Cf. A052016, A048398, A006055.

Cf. A138141. - Omar E. Pol, Dec 07 2008

A167842 Right-angled primes.

Original entry on oeis.org

101, 787, 12343, 34543, 54323, 56543, 654323, 1234543, 7654567, 345676543, 987654323, 32123456789, 34567876543, 654323456789

Offset: 1

Omar E. Pol, Nov 13 2009

Primes in A135602.

Primes whose structure of digits represents a right angle. The vertex is an internal digit. In the graphic representation the points are connected by imaginary line segments from left to right. This sequence is finite.

Cf. A135602, A048398.

More terms from Jens Kruse Andersen, Jun 26 2014

A052016 Primes with digits in descending order that differ exactly by 1.

Original entry on oeis.org

2, 3, 5, 7, 43, 76543

Offset: 1

Patrick De Geest, Nov 15 1999

Primes in A138142. - Omar E. Pol, Dec 07 2008

Cf. A052017, A048398, A006055, A138142.

fQ[n_]:=Module[{id=IntegerDigits[n],}, n < 10 || Union[Differences[id]] == {-1}]; Select[Prime[Range[10000]], fQ] (* Vladimir Joseph Stephan Orlovsky, Dec 29 2010 *)

A059170 Strictly undulating primes (digits alternate and differ by 1).

Original entry on oeis.org

2, 3, 5, 7, 23, 43, 67, 89, 101, 787, 32323, 78787, 1212121, 323232323, 989898989, 12121212121, 32323232323, 787878787878787878787, 787878787878787878787878787, 1212121212121212121212121212121212121212121

Offset: 1

N. J. A. Sloane, Feb 14 2001

Of form ababa... with |a-b| = 1.

The next two terms have 95 and 139 digits respectively. - Jayanta Basu, May 09 2013

C. A. Pickover, "Keys to Infinity", Wiley 1995, pp. 159-160.
C. A. Pickover, "Wonders of Numbers", Oxford New York 2001, Chapter 52, pp. 123-124, 316-317.

Harvey P. Dale, Table of n, a(n) for n = 1..25 (All terms with less than 1000 digits.)
Patrick De Geest, More undulating primes
C. A. Pickover, "Wonders of Numbers, Adventures in Mathematics, Mind and Meaning," Zentralblatt review

Cf. A032758, A059168, A048398, A033619, A046075, A059758.

a[n_]:=DeleteDuplicates[Take[IntegerDigits[n],{1,-1,2}]]; b[n_]:=DeleteDuplicates[Take[IntegerDigits[n],{2,-1,2}]]; t={}; Do[p=Prime[n]; If[p<10, AppendTo[t,p], If[Length[a[p]] == Length[b[p]] == 1 && Abs[a[p][[1]]-b[p][[1]]] == 1, AppendTo[t,p]]], {n,10^5}]; t (* Jayanta Basu, May 08 2013 *)
t1=Join[{2,3,5,7},Select[Range[10,100],PrimeQ[#]&&Abs[Differences[IntegerDigits[#]]]=={1}&]]; Do[a=n*10+(n-1);b=(n-1)*10+n; t1=Join[t1,Select[Table[(a*10^(2*n+1)-b)/99,{n,25}],PrimeQ]]; If[n<=7,c=n*10+(n+1);d=(n+1)*10+n;t1=Join[t1,Select[Table[(c*10^(2*n+1)-d)/99,{n,25}],PrimeQ]]],{n,1,9,2}]; Sort[t1] (* Jayanta Basu, May 09 2013 *)
 With[{c=Flatten[{#,Reverse[#]}&/@Table[{a,a+1},{a,0,8}],1]},Flatten[ Select[ Table[ FromDigits[PadRight[{},n,#]],{n,50}],PrimeQ]&/@c]]//Union (* Harvey P. Dale, Aug 20 2022 *)

Extended by Patrick De Geest, Feb 25 2001

Offset corrected by Arkadiusz Wesolowski, Sep 13 2011

A089291 Prime worms (as defined below).

Original entry on oeis.org

101, 787, 12101, 32323, 34543, 78787, 1012321, 1212121, 3212123, 3212323, 3454343, 7654567, 7656787, 7676567, 7678787, 7876567, 7898767, 101012321, 101210101, 101232121, 121232101, 123210121, 123232121, 321234343, 323232323

Offset: 1

Enoch Haga, Dec 23 2003

By analogy, primes of this type are worms with a head and tail and body composed of the same digit which weaves in and out of the prime. In a(2)=12101 the worm is defined by the digit 1.

			a(2)=12101 because that number is prime with identical first and last digits. Then abs(1-2)=1; abs(2-1)=1; abs(1-0)=1; abs(0-1)=1; and sum of absolute values is 4, one less than the 5 digits in the prime.

The concept is due to Carlos Rivera in his Puzzle 246 (where he asks for the first pandigital prime worm and for the first pandigital titanic prime worm - solutions are at his site).

Carlos Rivera, Puzzle 246. The worms

This is a subset of A048398. Cf. A089315-A089317, A048398-A048405.

Primes whose first and last digits are identical and whose successive digit differences have a uniformly absolute value of 1. Thus the sum of absolute values is one less than the number of digits in the prime. No two adjacent digits are identical or differ by more than one.

Edited by Charles R Greathouse IV, Aug 02 2010

A089315 Prime worms [successive digit differences with absolute value of 3].

Original entry on oeis.org

14741, 74747, 1414741, 1474141, 14141414141, 14141414741, 14141474741, 14147414741, 14147474141, 74141414147, 1474741414141, 7474141474747, 7474741414747, 14141474141414141, 14147414747474741, 14147474147474741

Offset: 0

Enoch Haga, Dec 25 2003

One of a family of prime worms differing according to the uniform absolute value of successive digit pairs. Sequence checked to 10^9.

This is a subset of A048400. Cf. A089291, A089316-A089317, A048398-A048405.

			a(1)=74747 because the number is prime, has identical first and last digits and abs(7-4)=3; abs(4-7)=3; abs(7-4)=3 and abs(4-7)=3. In this number, the worm is 7.

Carlos Rivera's primepuzzles.net, Puzzle 246.

Carlos Rivera, Puzzle 246. The worm

Select prime numbers having the same first and last digits; if the uniform absolute value of successive digit differences is 3, add to sequence.

More terms from David Wasserman, Sep 09 2005

A089317 Prime worms [successive digit differences with absolute value of 4].

Original entry on oeis.org

151, 373, 95959, 9515959, 159595151, 159595951, 15151595951, 15951595151, 95951515159, 1515159515951, 1515959515951, 1515959595151, 1595159515151, 1595159595151, 9515151515159, 9515159515159, 9515159595959, 9595159515959

Offset: 0

Enoch Haga, Dec 25 2003

			a(1)=373; first and last digits are 3; abs(3-7)=4; abs(7-3)=4; the worm is 3.

Carlos Rivera's primepuzzles.net, Puzzle 246

Carlos Rivera, Puzzle 246. The worm

This is a subsequence of A048401. Cf. A089291, A089315-A089316, A048398-A048405.

Select prime numbers having the same first and last digits; if the uniform absolute value of successive digit differences is 4, add to sequence.

More terms from David Wasserman, Sep 09 2005

A089316 Prime worms [successive digit differences with absolute value of 2].

Original entry on oeis.org

131, 313, 353, 757, 797, 35353, 35753, 75797, 79757, 97579, 3131353, 3135313, 3531313, 7535797, 313131353, 313135313, 313579753, 353535313, 357531313, 357531353, 357535753, 357575753, 357975353, 753535357, 757975357, 975353579

Offset: 0

Enoch Haga, Dec 25 2003

			a(4)=797; first and last digits are 7; abs(7-9)=2; abs(9-7)=2; the worm is 7.

Carlos Rivera, Puzzle 246. The worm, The Prime Puzzles and Problems Connection.

Cf. A089291.

This is a subset of A048399. Cf. A089291, A089315, A089317, A048398-A048405.

pwQ[n_]:=Module[{idn=IntegerDigits[n]},First[idn]==Last[idn]&&Union[Abs[ Differences[idn]]]=={2}]; Select[Prime[Range[50000000]],pwQ] (* Harvey P. Dale, Mar 26 2013 *)

Select prime numbers having the same first and last digits; if the uniform absolute value of successive digit differences is 2, add to sequence.

cp's OEIS Frontend

A048404 Primes with consecutive digits that differ exactly by 7.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

A048403 Primes with consecutive digits that differ exactly by 6.

Views

Author

Keywords

Comments

Crossrefs

Programs

PARI

Extensions

A052017 Primes with digits in ascending order that differ exactly by 1.

Views

Author

Keywords

Comments

Crossrefs

A167842 Right-angled primes.

Views

Author

Keywords

Comments

Crossrefs

Extensions

A052016 Primes with digits in descending order that differ exactly by 1.

Views

Author

Keywords

Comments

Crossrefs

Programs

Mathematica

A059170 Strictly undulating primes (digits alternate and differ by 1).

Views

Author

Keywords

Comments

References

Links

Crossrefs

Programs

Mathematica

Extensions

A089291 Prime worms (as defined below).

Views

Author

Keywords

Comments

Examples

References

Links

Crossrefs

Formula

Extensions

A089315 Prime worms [successive digit differences with absolute value of 3].

Views

Author

Keywords

Comments

Examples

References

Links

Formula

Extensions

A089317 Prime worms [successive digit differences with absolute value of 4].

Views

Author

Keywords

Examples

References

Links

Crossrefs