A067254 Numbers k such that the decimal encoding of the prime factorization of k (A067599) ends in k.

11, 8571, 11371, 190911, 12711811, 14713491, 19090911, 71119711, 12531135391, 15311195711, 112717566411, 158318548011, 518914376931, 7292811659931

Offset: 1

Author

Joseph L. Pe, Feb 20 2002

Keywords

• base
• nonn
• more

Comments

a(13) > 2*10^11. 518914376931, 7292811659931, 19090909090909090911 and prime repunits (A004022) are also terms. - Donovan Johnson, Dec 04 2012

Are there any terms not ending in 1? Equivalently, are any terms also in A070003? - Charles R Greathouse IV, Dec 05 2012

a(15) > 10^13. If exponents equal to 1 are not represented (as in A080670), the corresponding sequence starts with 113113, 31373137, and 533517177839 = 853 * 3517 * 177839. - Giovanni Resta, Jun 26 2017

Examples

			The prime factorization of 190911 is 3^1 * 7^1 * 9091^1 with decimal encoding 317190911, which ends in 190911. Hence 190911 is a term of the sequence.
		

Crossrefs

Cf. A004022, A067599, A070003, A080670.

Programs

Mathematica

(*returns true if a ends with b, false o.w.*) f[a_, b_] := Module[{c, d, e, g, h, i, r}, r = False; c = ToString[a]; d = ToString[b]; e = StringLength[c]; g = StringPosition[c, d]; h = Length[g]; If[h > 0, i = g[[h]]; If[i[[2]] == e, r = True]]; r]; (*gives the decimal encoding of the prime factorization of n*) g[n_] := FromDigits[Flatten[IntegerDigits[FactorInteger[n]]]]; Do[If[f[g[n], n], Print[n]], {n, 1, 10^6} ]

PARI

{a067254(a,b) = local(n,v,k,j); for(n=max(2,a),b,v=factor(n); if(eval(concat(vector(matsize(v)[1],k, concat(vector(matsize(v)[2],j,Str(v[k,j]))))))%(10^length(Str(n)))==n,print1(n,",")))}
a067254(2,2*10^7) \\ Klaus Brockhaus, Feb 22 2002

Extensions

a(5)-a(7) from Klaus Brockhaus, Feb 22 2002

a(8)-a(10) from Donovan Johnson, Mar 26 2010

a(11)-a(12) from Donovan Johnson, Dec 04 2012

a(13) from Giovanni Resta, Jun 09 2017

a(14) from Giovanni Resta, Jun 26 2017