A071119 Palindromic primes in which deleting the outside pair of digits yields a prime at every stage until finally a single-digit prime is obtained.

2, 3, 5, 7, 131, 151, 353, 373, 727, 757, 929, 11311, 31513, 33533, 37273, 37573, 39293, 71317, 93739, 97579, 1335331, 3315133, 3392933, 7392937, 9375739, 373929373, 733929337

Offset: 1

Author

Lior Manor, May 28 2002

Keywords

• base
• easy
• fini
• full
• nonn

Examples

			31513 is in the sequence because 31513, 151 and 5 are primes.
a(17) = 39293 because 39293, 929 and 2 are primes.
		

References

• J.-P. Delahaye, "Pour la science", (French edition of Scientific American), Juin 2002, p. 99.
• G. L. Honaker, Jr. and C. Caldwell, Palindromic prime pyramids, J. Recreational Mathematics, vol. 30.3, pp. 169-176, 1999-2000.

Links

• G. L. Honaker, Jr. and C. K. Caldwell, Palindromic Prime Pyramids
• G. L. Honaker, Jr. and C. K. Caldwell, Supplement to "Palindromic Prime Pyramids"
• I. Peterson, MathTrek, Primes, Palindromes and Pyramids

Crossrefs

Cf. A002385.

Programs

PARI

V = [2, 3, 5, 7]; vCount = 4; x = [1, 3, 7, 9]; print(V); forstep (i = 2, 20, 2, newV = vector(4*vCount); newCount = 0; for (j = 1, 4, for (k = 1, vCount, n = x[j]*(10^i + 1) + 10*V[k]; if (isprime(n), print(n); newCount = newCount + 1; newV[newCount] = n))); V = newV; vCount = newCount) \\ David Wasserman, Oct 04 2004

Extensions

Edited by N. J. A. Sloane at the suggestion of Andrew S. Plewe, May 14 2007