A256957 -id:A256957

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A046210

Erroneous version of A256957.

+20
0

11, 131, 2, 929, 10301, 16361, 10281118201, 35605550653, 7159123219517

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

OFFSET

1,1

LINKS

Table of n, a(n) for n=1..9.

KEYWORD

dead

STATUS

approved

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

A034276

Smallest prime that generates a prime pyramid of height n.

+10
3

11, 29, 2, 5, 41, 251, 43, 145577, 51941, 4372877, 26901631, 366636187, 15387286403, 218761753811, 3313980408469

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

OFFSET

1,1

COMMENTS

Let p be prime; look for the smallest prime in {1|p|1, 3|p|3, 7|p|7, 9|p|9}, where '|' stands for concatenation; repeat until no such prime can be found; then height(p) = number of rows in pyramid.

a(13) > 10^10. - Donovan Johnson, Aug 13 2010

LINKS

Table of n, a(n) for n=1..15.

H. Heinz, Patterns in Primes, Illustrating Two Prime 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

Example for p=43: 43 3433 334333 93343339 3933433393 939334333939 39393343339393, stop; height(43)=7.

CROSSREFS

Cf. A047076, A053600, A052205, A256957, A052091, A052092.

KEYWORD

nonn,nice,base,more

AUTHOR