A068150 -id:A068150 - cp's OEIS frontend

A057626 Initial prime in first sequence of n primes congruent to 2 modulo 5.

2, 337, 1627, 57427, 192637, 776257, 15328637, 70275277, 244650317, 452942827, 452942827, 73712513057, 319931193737, 2618698284817, 10993283241587, 54010894438097, 101684513099627, 196948379177587

Offset: 1

Robert G. Wilson v, Oct 09 2000

nonn

Same as A068150 except a(1). - Jens Kruse Andersen, Jun 03 2006

			a(5) = 192637 because this number is the first in a sequence of 5 consecutive primes all of the form 5n + 2.

J. K. Andersen, Consecutive Congruent Primes.

NextPrime[ n_Integer ] := Module[ {k = n + 1}, While[ ! PrimeQ[ k ], k++ ]; Return[ k ] ]; PrevPrime[ n_Integer ] := Module[ {k = n - 1}, While[ ! PrimeQ[ k ], k-- ]; Return[ k ] ]; p = 0; Do[ a = Table[ -1, {n} ]; k = Max[ 1, p ]; While[ Union[ a ] != {2}, k = NextPrime[ k ]; a = Take[ AppendTo[ a, Mod[ k, 5 ] ], -n ] ]; p = NestList[ PrevPrime, k, n ]; Print[ p[ [ -2 ] ] ]; p = p[ [ -1 ] ], {n, 1, 9} ]
Module[{nn=13410000,pr5},pr5=Table[If[Mod[p,5]==2,1,0],{p,Prime[Range[nn]]}];Prime/@ Table[SequencePosition[pr5,PadRight[{},n,1],1],{n,8}]][[;;,1,1]] (* The program generates the first 8 terms of the sequence. *) (* Harvey P. Dale, Jan 07 2024 *)

More terms from Jens Kruse Andersen, Jun 03 2006

a(15)-a(18) from Giovanni Resta, Aug 04 2013

A057636 Initial prime in first sequence of n primes congruent to 4 modulo 5. The first prime in a sequence of length n all ending with the digit 9.

Original entry on oeis.org

19, 139, 3089, 18839, 123229, 2134519, 12130109, 23884639, 363289219, 9568590299, 24037796539, 130426565719, 405033487139, 3553144754209, 4010803176619, 71894236537009, 71894236537009

Offset: 1

Robert G. Wilson v, Oct 10 2000

nonn

			a(5) = 123229 because this number is the first in a sequence of 5 consecutive primes all of the form 5n + 4.

J. K. Andersen, Consecutive Congruent Primes.

Cf. A054681, A057618, A057631, A068150.

NextPrime[ n_Integer ] := Module[ {k = n + 1}, While[ ! PrimeQ[ k ], k++ ]; Return[ k ] ]; PrevPrime[ n_Integer ] := Module[ {k = n - 1}, While[ ! PrimeQ[ k ], k-- ]; Return[ k ] ]; p = 0; Do[ a = Table[ -1, {n} ]; k = Max[ 1, p ]; While[ Union[ a ] != {4}, k = NextPrime[ k ]; a = Take[ AppendTo[ a, Mod[ k, 5 ] ], -n ] ]; p = NestList[ PrevPrime, k, n ]; Print[ p[ [ -2 ] ] ]; p = p[ [ -1 ] ], {n, 1, 9} ]

Phil Carmody gives a(15)= 4010803176619 in A054681
More terms from Jens Kruse Andersen, Jun 03 2006
a(16)-a(17) from Giovanni Resta, Aug 01 2013

cp's OEIS Frontend

A057626 Initial prime in first sequence of n primes congruent to 2 modulo 5.

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