A034276 -id:A034276

The OEIS is supported by the many generous donors to the OEIS Foundation.

Search: a034276 -id:a034276

Displaying 1-3 of 3 results found.

page 1

A053600

a(1) = 2; for n>=1, a(n+1) is the smallest palindromic prime with a(n) as a central substring.

+10
12

2, 727, 37273, 333727333, 93337273339, 309333727333903, 1830933372733390381, 92183093337273339038129, 3921830933372733390381293, 1333921830933372733390381293331, 18133392183093337273339038129333181

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

REFERENCES

G. L. Honaker, Jr. and Chris K. Caldwell, Palindromic Prime Pyramids, J. Recreational Mathematics, Vol. 30(3) 169-176, 1999-2000.

LINKS

Clark Kimberling, Table of n, a(n) for n = 1..200

P. De Geest, Palindromic Prime Pyramid Puzzle by G.L.Honaker,Jr

G. L. Honaker, Jr. and Chris Caldwell, Prime Curios! 18133...33181 (35-digits)

G. L. Honaker, Jr. & C. K. Caldwell, Palindromic Prime Pyramids

G. L. Honaker, Jr. & C. K. Caldwell, Supplement to "Palindromic Prime Pyramids"

Ivars Peterson, Primes, Palindromes, and Pyramids, Science News.

Inder J. Taneja, Palindromic Prime Embedded Trees, RGMIA Res. Rep. Coll. 20 (2017), Art. 124.

Inder J. Taneja, Same Digits Embedded Palprimes, RGMIA Research Report Collection (2018) Vol. 21, Article 75, 1-47.

EXAMPLE

As a triangle:

.........2

........727

.......37273

.....333727333

....93337273339

..309333727333903

1830933372733390381

MATHEMATICA

d[n_] := IntegerDigits[n]; t = {x = 2}; Do[i = 1; While[! PrimeQ[y = FromDigits[Flatten[{z = d[i], d[x], Reverse[z]}]]], i++]; AppendTo[t, x = y], {n, 10}]; t (* Jayanta Basu, Jun 24 2013 *)

PROG

(Python)

from gmpy2 import digits, mpz, is_prime

A053600_list, p = [2], 2

for _ in range(30):

....m, ps = 1, digits(p)

....s = mpz('1'+ps+'1')

....while not is_prime(s):

........m += 1

........ms = digits(m)

........s = mpz(ms+ps+ms[::-1])

....p = s

....A053600_list.append(int(p)) # Chai Wah Wu, Apr 09 2015

CROSSREFS

Cf. A000040, A002385, A047076, A052205, A034276, A256957, A052091, A052092, A261881.

KEYWORD

base,nonn

AUTHOR

G. L. Honaker, Jr., Jan 20 2000

STATUS

approved

A052205

a(n+1) is smallest palindromic prime containing exactly 3 more digits on each end than the previous term, with a(n) as a central substring.

+10
7

2, 1022201, 1051022201501, 1241051022201501421, 1071241051022201501421701, 1051071241051022201501421701501, 1091051071241051022201501421701501901, 1351091051071241051022201501421701501901531

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

Giovanni Resta, Table of n, a(n) for n = 1..26 (full sequence)

CROSSREFS

Cf. A047076, A053600, A034276, A256957, A052091, A052092.

KEYWORD

base,nonn,fini,full

AUTHOR

G. L. Honaker, Jr., Jan 28 2000

EXTENSIONS

Shown to be finite by Felice Russo

STATUS

approved

A256957

Smallest palindromic prime that generates a palindromic prime pyramid of height n.

+10
4

11, 131, 2, 5, 10301, 16361, 10281118201, 35605550653, 7159123219517, 17401539893510471, 3205657651567565023

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

Start with a palindromic prime p; look for smallest palindromic prime that has previous term as a centered substring and has 2 more digits (i.e., one more digit at each end); repeat until no such palindromic prime can be found; then height(p) = number of rows in pyramid. Each row of pyramid must be the smallest prime that can be used. Then a(n) = smallest value of p that generates a pyramid of height n.

LINKS

Table of n, a(n) for n=1..11.

G. L. Honaker, Jr. and Chris K. Caldwell, Palindromic prime pyramids

Ivars Peterson's MathTrek, Primes, Palindromes, and Pyramids

Chai Wah Wu, On a conjecture regarding primality of numbers constructed from prepending and appending identical digits, arXiv:1503.08883 [math.NT], 2015.

EXAMPLE

a(1) = 11.

a(4) = 5:

151

31513

3315133, stop;

height(5)=4.

a(6)=16362:

16361

1163611

311636113

33116361133

3331163611333

333311636113333, stop;

height(16361)=6.

CROSSREFS

Cf. A034276, A052205, A053600.

KEYWORD

nonn,base,more

AUTHOR

Felice Russo, Jan 25 2000

EXTENSIONS

Added a(10)-a(11) and corrected a(4) - Chai Wah Wu, Apr 09 2015

Entry revised by N. J. A. Sloane, Apr 13 2015

STATUS

approved

page 1

Search completed in 0.005 seconds