A030670 -id:A030670 - cp's OEIS frontend

A064735 Next prime containing prime(n) in decimal notation.

23, 13, 53, 17, 113, 113, 173, 191, 223, 229, 131, 137, 241, 431, 347, 353, 359, 461, 167, 271, 173, 179, 283, 389, 197, 1013, 1031, 5107, 1091, 2113, 1277, 1319, 1373, 1399, 1493, 1151, 1571, 1163, 3167, 1733, 2179, 1181, 1913, 1193, 1973, 1993, 2111

Offset: 1

Reinhard Zumkeller, Oct 17 2001

Harry J. Smith, Table of n, a(n) for n=1..1000

Cf. A062584, A030670, A000040, A252629.

a(n)={ my(q=prime(n), m=10^(logint(q,10)+1)); forprime(p=m, oo, my(x=p); while(x>=q, if(x%m==q, return(p)); x\=10)) } \\ Harry J. Smith, Sep 24 2009

a(n) = A252629(n) + prime(n). - Zak Seidov, Dec 19 2014

A065112 Smallest prime whose decimal expansion ends (nontrivially) with the n-th prime; or 0 if no such prime exists.

Original entry on oeis.org

0, 13, 0, 17, 211, 113, 317, 419, 223, 229, 131, 137, 241, 443, 347, 353, 359, 461, 167, 271, 173, 179, 283, 389, 197, 5101, 1103, 5107, 1109, 2113, 4127, 2131, 2137, 4139, 11149, 1151, 4157, 1163, 3167, 6173, 2179, 1181, 3191, 1193, 5197, 6199, 4211

Offset: 1

Robert G. Wilson v, Nov 12 2001

a(1) and a(3) (respectively for primes 2 and 5) are trivially zero. All other terms are nonzero by Dirichlet's theorem on arithmetic progressions. - Joerg Arndt, Jun 06 2021

Daniel Mondot, Table of n, a(n) for n = 1..10000
Wikipedia, Dirichlet's theorem on arithmetic progressions

Cf. A030670.

f[n_] := (k = 1; While[a = ToExpression[ ToString[k] <> ToString[n]]; ! PrimeQ[a], k++ ]; a); Table[ f[ Prime[n]], {n, 4, 50} ]

A064792 Append more digits to the n-th prime (leading zeros are permitted) until another prime is reached.

Original entry on oeis.org

23, 31, 53, 71, 113, 131, 173, 191, 233, 293, 311, 373, 419, 431, 479, 5303, 593, 613, 673, 719, 733, 797, 839, 8923, 971, 1013, 1031, 10709, 1091, 11311, 1277, 1319, 1373, 1399, 1493, 1511, 1571, 1637, 16703, 1733, 17903, 1811, 1913, 1931, 1973

Offset: 1

Reinhard Zumkeller, Oct 17 2001

Differs from A030670 in that here the appended digits may start with 0 which is not possible there (although zeros are allowed there, too, if they are not the first appended digit): The first difference appears at a(16) = 5303 where A030670(16) = 5323. - M. F. Hasler, Jan 15 2025

Daniel Mondot, Table of n, a(n) for n = 1..10000

Cf. A030665.

See A030670 for another version. Note that A030670 >= a(n). Cf. A065112.

apply( {A064792(n)=n=prime(n);for(L=1,oo, n*=10; forstep(s=1,10^L-1,2, isprime(n+s)&& return(n+s)))}, [1..44]) \\ M. F. Hasler, Jan 15 2025

a(n) = A030665(prime(n)). - Michel Marcus, Jan 17 2025

A178220 Smallest number that appending to n-th prime gives another prime.

Original entry on oeis.org

3, 1, 3, 1, 3, 1, 3, 1, 3, 3, 1, 3, 9, 1, 9, 23, 3, 3, 3, 9, 3, 7, 9, 23, 1, 3, 1, 11, 1, 11, 7, 9, 3, 9, 3, 1, 1, 7, 29, 3, 11, 1, 3, 1, 3, 3, 1, 7, 3, 3, 3, 3, 1, 11, 9, 3, 3, 1, 7, 9, 3, 9, 9, 9, 7, 21, 3, 1, 21, 1, 3, 3, 1, 3, 3, 3, 17, 19, 3, 1, 11, 1, 17, 7, 1, 51, 3, 37, 33, 7

Offset: 1

Zak Seidov, Dec 20 2010

			n=1: prime(1)=2, A030670(1)=23, after deleting 2 we get a(1)=3
n=2: prime(2)=3, A030670(2)=31, after deleting 3 we get a(2)=1

Cf. A030670.

f[n_] := (k = 1; tsn = ToString[n]; While[a = ToExpression[tsn <> ToString[k]]; !PrimeQ[a], k++]; k);
Table[f[Prime[n]], {n, 1, 200}]

a(n) = A030670(n) after deleting n-th prime.

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A064735 Next prime containing prime(n) in decimal notation.

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A065112 Smallest prime whose decimal expansion ends (nontrivially) with the n-th prime; or 0 if no such prime exists.

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A064792 Append more digits to the n-th prime (leading zeros are permitted) until another prime is reached.

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PARI

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A178220 Smallest number that appending to n-th prime gives another prime.

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Mathematica

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